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1
Basalamah, Doaa. "Statistical Inference for a New Class of Skew t Distribution and Its Related Properties." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1496762068499547.
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Lima, Stênio Rodrigues. "The half-normal generalized family and Kumaraswamy Nadarajah-Haghighi distribution." Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/14917.
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CAPES
As distribuições generalizadas têm sido amplamente estudadas na Estatística e diversos autores têm investigado novas distribuições de sobrevivência devido a sua flexibilidade para ajustar dados. Neste trabalho um novo método de compor distribuições é proposto: a família Half-Normal-G, em que G e chamada distribuição baseline. Demostramos que as funções densidades das distribuiçõess propostas podem ser expressas como combinação linear de funções densidades das respectivas exponencializadas-G. Diversas propriedades dessa família são estudadas. Apresentamos também uma nova distribuição de probabilidade baseado na Família de Distribuições Generalizadas Kumaraswamy (kw- G), j a conhecida na literatura. Escolhemos como baseline a distribuição Nadarajah- Haghighi, recentemente estudada por Nadarajah e Haghighi (2011) e que desenvolveram algumas propriedades interessantes. Estudamos várias propriedades da nova distribuição Kumaraswamu-Nadarajah-Haghighi (Kw-NH) e fizemos duas aplicações de bancos de dados mostrando empiricamente a flexibilidade do modelo.
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Kam, Po-ling, and 甘寶玲. "Mixture autoregression with heavy-tailed conditional distribution." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29614922.
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Wei, Yan. "Robust mixture regression models using t-distribution." Kansas State University, 2012. http://hdl.handle.net/2097/14110.
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Master of ScienceDepartment of Statistics
Weixin Yao
In this report, we propose a robust mixture of regression based on t-distribution by extending the mixture of t-distributions proposed by Peel and McLachlan (2000) to the regression setting. This new mixture of regression model is robust to outliers in y direction but not robust to the outliers with high leverage points. In order to combat this, we also propose a modified version of the proposed method, which fits the mixture of regression based on t-distribution to the data after adaptively trimming the high leverage points. We further propose to adaptively choose the degree of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degree of freedom. We demonstrate the effectiveness of the proposed new method and compare it with some of the existing methods through simulation study.
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Xing, Yanru. "Robust mixture regression model fitting by Laplace distribution." Kansas State University, 2013. http://hdl.handle.net/2097/16534.
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Master of ScienceDepartment of Statistics
Weixing Song
A robust estimation procedure for mixture linear regression models is proposed in this report by assuming the error terms follow a Laplace distribution. EM algorithm is imple- mented to conduct the estimation procedure of missing information based on the fact that the Laplace distribution is a scale mixture of normal and a latent distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in this literature. A sensitivity study is also conducted based on a real data example to illustrate the application of the proposed method.
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Liu, Yantong. "Robust mixture linear EIV regression models by t-distribution." Kansas State University, 2012. http://hdl.handle.net/2097/15157.
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Master of ScienceDepartment of Statistics
Weixing Song
A robust estimation procedure for mixture errors-in-variables linear regression models is proposed in the report by assuming the error terms follow a t-distribution. The estimation procedure is implemented by an EM algorithm based on the fact that the t-distribution is a scale mixture of normal distribution and a Gamma distribution. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies. Comparison is also made with the MLE procedure under normality assumption.
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Zhang, Jingyi. "Robust mixture regression modeling with Pearson type VII distribution." Kansas State University, 2013. http://hdl.handle.net/2097/15648.
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Master of ScienceDepartment of Statistics
Weixing Song
A robust estimation procedure for parametric regression models is proposed in the paper by assuming the error terms follow a Pearson type VII distribution. The estimation procedure is implemented by an EM algorithm based on the fact that the Pearson type VII distributions are a scale mixture of a normal distribution and a Gamma distribution. A trimmed version of proposed procedure is also discussed in this paper, which can successfully trim the high leverage points away from the data. Finite sample performance of the proposed algorithm is evaluated by some extensive simulation studies, together with the comparisons made with other existing procedures in the literature.
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Karaiskos, Ilias-Efstratios. "Spray structure and mixture distribution in direct-injection gasoline engines." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417137.
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Kampanis, Nicholas. "Flow, mixture distribution and combustion in five-valve gasoline engines." Thesis, Imperial College London, 2003. http://hdl.handle.net/10044/1/8338.
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Assis, Alice Nascimento de, and 92-99331-6592. "Um modelo multivariado para predição de taxas e proporções dependentes." Universidade Federal do Amazonas, 2018. https://tede.ufam.edu.br/handle/tede/6391.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Relative humidity interferes in many aspects in the life of the human being, and due to the many consequences that a low or a high percentage can entail, the control of its level is of paramount importance. Thus, the modeling of extreme situations of this variable can aid in the planning of human activities that are susceptible to their harmful effects, such as public health. The main interest is to predict, based on probability density functions applied to observed data, the values that may occur in a certain locality. The Generalized Distribution of Extreme Values has been widely used for this purpose and research using Time Series analysis of meteorological and climatic data. In this work, a statistical model is proposed for prediction of rates and temporal proportions and/or spatially dependents. The model was constructed by marginalizing the Kumaraswamy G-exponentialised distribution conditioned to a random field with positive alpha-stable distribution. Some properties of this model were presented, procedures for estimation and inference were discussed and an MCEM algorithm was developed to estimate the parameters. As a particular case, the model was used for spatial prediction of relative humidity in weather stations at Amazonas state, Brazil.
A umidade relativa interfere em vários aspectos na vida do ser humano, e devido as muitas consequências que um baixo ou um alto percentual podem acarretar, o controle de seu nível é de suma importância. Dessa forma, a modelagem de situações extremas dessa variável pode auxiliar no planejamento de atividades humanas que sejam suscetíveis aos seus efeitos danosos, como a saúde pública. O principal interesse é prever com base em funções densidade de probabilidade aplicadas aos dados observados, os valores que possam ocorrer em uma certa localidade. A distribuição Generalizada de Valores Extremos tem sido amplamente utilizada com essa finalidade e pesquisas utilizando análise de Séries Temporais de dados meteorológicos e climáticos. Neste trabalho, é proposto um modelo estatístico para predição de taxas e proporções temporais e/ou espacialmente dependentes. O modelo foi construído através da marginalização da distribuição Kumaraswamy G-exponencializada condicionada a um campo aleatório com distribuição alfaestável positivo. Algumas propriedades desse modelo foram apresentadas, procedimentos para estimação e inferência foram discutidos e um algoritmo MCEM foi desenvolvido parar estimar os parâmetros. Como um caso particular, o modelo foi utilizado para predição espacial da umidade relativa do ar observada nas estações meteorológicas do Estado do Amazonas.
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Chang, Ilsung. "Bayesian inference on mixture models and their applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/3990.
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Mixture models are useful in describing a wide variety of random phenomena because
of their flexibility in modeling. They have continued to receive increasing attention
over the years from both a practical and theoretical point of view. In their applications,
estimating the number of mixture components is often the main research
objective or the first step toward it. Estimation of the number of mixture components
heavily depends on the underlying distribution. As an extension of normal
mixture models, we introduce a skew-normal mixture model and adapt the reversible
jump Markov chain Monte Carlo algorithm to estimate the number of components
with some applications to biological data.
The reversible jump algorithm is also applied to the Cox proportional hazard
model with frailty. We consider a regression model for the variance components in
the proportional hazards frailty model. We propose a Bayesian model averaging procedure
with a reversible jump Markov chain Monte Carlo step which selects the model
automatically. The resulting regression coefficient estimates ignore the model uncertainty
from the frailty distribution. Finally, the proposed model and the estimation
procedure are illustrated with simulated example and real data.
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Li, Xiongya. "Robust multivariate mixture regression models." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38427.
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Doctor of PhilosophyDepartment of Statistics
Weixing Song
In this dissertation, we proposed a new robust estimation procedure for two multivariate mixture regression models and applied this novel method to functional mapping of dynamic traits. In the first part, a robust estimation procedure for the mixture of classical multivariate linear regression models is discussed by assuming that the error terms follow a multivariate Laplace distribution. An EM algorithm is developed based on the fact that the multivariate Laplace distribution is a scale mixture of the multivariate standard normal distribution. The performance of the proposed algorithm is thoroughly evaluated by some simulation and comparison studies. In the second part, the similar idea is extended to the mixture of linear mixed regression models by assuming that the random effect and the regression error jointly follow a multivariate Laplace distribution. Compared with the existing robust t procedure in the literature, simulation studies indicate that the finite sample performance of the proposed estimation procedure outperforms or is at least comparable to the robust t procedure. Comparing to t procedure, there is no need to determine the degrees of freedom, so the new robust estimation procedure is computationally more efficient than the robust t procedure. The ascent property for both EM algorithms are also proved. In the third part, the proposed robust method is applied to identify quantitative trait loci (QTL) underlying a functional mapping framework with dynamic traits of agricultural or biomedical interest. A robust multivariate Laplace mapping framework was proposed to replace the normality assumption. Simulation studies show the proposed method is comparable to the robust multivariate t-distribution developed in literature and outperforms the normal procedure. As an illustration, the proposed method is also applied to a real data set.
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Ngundze, Unathi. "Statistical comparison of international size-based equity index using a mixture distribution." Thesis, Nelson Mandela Metropolitan University, 2011. http://hdl.handle.net/10948/d1012367.
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Investors and financial analysts spend an inordinate amount of time, resources and effort in an attempt to perfect the science of maximising the level of financial returns. To this end, the field of distribution modelling and analysis of firm size effect is important as an investment analysis and appraisal tool. Numerous studies have been conducted to determine which distribution best fits stock returns (Mandelbrot, 1963; Fama, 1965 and Akgiray and Booth, 1988). Analysis and review of earlier research has revealed that researchers claim that the returns follow a normal distribution. However, the findings have not been without their own limitations in terms of the empirical results in that many also say that the research done does not account for the fat tails and skewness of the data. Some research studies dealing with the anomaly of firm size effect have led to the conclusion that smaller firms tend to command higher returns relative to their larger counterparts with a similar risk profile (Banz, 1981). Recently, Janse van Rensburg et al. (2009a) conducted a study in which both non- normality of stock returns and firm size effect were addressed simultaneously. They used a scale mixture of two normal distributions to compare the stock returns of large capitalisation and small capitalisation shares portfolios. The study concluded that in periods of high volatility, the small capitalisation portfolio is far more risky than the large capitalisation portfolio. In periods of low volatility they are equally risky. Janse van Rensburg et al. (2009a) identified a number of limitations to the study. These included data problems, survivorship bias, exclusion of dividends, and the use of standard statistical tests in the presence of non-normality. They concluded that it was difficult to generalise findings because of the use of only two (limited) portfolios. In the extension of the research, Janse van Rensburg (2009b) concluded that a scale mixture of two normal distributions provided a more superior fit than any other mixture. The scope of this research is an extension of the work by Janse van Rensburg et al. (2009a) and Janse van Rensburg (2009b), with a view to addressing several of the limitations and findings of the earlier studies. The Janse van rensburg (2009b) study was based on data from the Johannesburg Stock Exchange (JSE); this study seeks to compare their research by looking at the New York Stock Exchange (NYSE) to determine if similar results occur in developed markets. For analysis purposes, this study used the statistical software package R (R Development Core Team 2008) and its package mixtools (Young, Benaglia, Chauveau, Elmore, Hettmansperg, Hunter, Thomas, Xuan 2008). Some computation was also done using Microsoft Excel. This dissertation is arranged as follows: Chapter 2 is a literature review of some of the baseline studies and research that supports the conclusion that earlier research finding had serious limitations. Chapter 3 describes the data used in the study and gives a breakdown of portfolio formation and the methodology used in the study. Chapter 4 provides the statistical background of the methods used in this study. Chapter 5 presents the statistical analysis and distribution fitting of the data. Finally, Chapter 6 gives conclusions drawn from the results obtained in the analysis of data as well as recommendations for future work.
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Pfister, Mark. "Distribution of a Sum of Random Variables when the Sample Size is a Poisson Distribution." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3459.
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A probability distribution is a statistical function that describes the probability of possible outcomes in an experiment or occurrence. There are many different probability distributions that give the probability of an event happening, given some sample size n. An important question in statistics is to determine the distribution of the sum of independent random variables when the sample size n is fixed. For example, it is known that the sum of n independent Bernoulli random variables with success probability p is a Binomial distribution with parameters n and p: However, this is not true when the sample size is not fixed but a random variable. The goal of this thesis is to determine the distribution of the sum of independent random variables when the sample size is randomly distributed as a Poisson distribution. We will also discuss the mean and the variance of this unconditional distribution.
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Wong, Po-shing, and 黃寶誠. "Some mixture models for the joint distribution of stock's return and trading volume." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31210065.
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Wong, Po-shing. "Some mixture models for the joint distribution of stock's return and trading volume /." [Hong Kong] : University of Hong Kong, 1991. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13009485.
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Kelbick, Nicole DePriest. "Detecting underlying emotional sensitivity in bereaved children via a multivariate normal mixture distribution." Columbus, Ohio : Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc%5fnum=osu1064331329.
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Thesis (Ph. D.)--Ohio State University, 2003.Title from first page of PDF file. Document formatted into pages; contains xiv, 122 p.; also contains graphics. Includes abstract and vita. Advisor: Joseph, Dept. of Statistics. Includes bibliographical references (p. 119-122).
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El, Zaart Ali. "Statistical inference and distribution selection for SAR image analysis : a mixture-based approach." Thèse, Sherbrooke : Université de Sherbrooke, 2001. http://savoirs.usherbrooke.ca/handle/11143/5001.
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Eljabri, Sumaya Saleh M. "New statistical models for extreme values." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/new-statistical-models-for-extreme-values(12e1ec08-dc66-4f20-a7dc-c89be62421a0).html.
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Extreme value theory (EVT) has wide applicability in several areas like hydrology, engineering, science and finance. Across the world, we can see the disruptive effects of flooding, due to heavy rains or storms. Many countries in the world are suffering from natural disasters like heavy rains, storms, floods, and also higher temperatures leading to desertification. One of the best known extraordinary natural disasters is the 1931 Huang He flood, which led to around 4 millions deaths in China; these were a series of floods between Jul and Nov in 1931 in the Huang He river.Several publications are focused on how to find the best model for these events, and to predict the behaviour of these events. Normal, log-normal, Gumbel, Weibull, Pearson type, 4-parameter Kappa, Wakeby and GEV distributions are presented as statistical models for extreme events. However, GEV and GP distributions seem to be the most widely used models for extreme events. In spite of that, these models have been misused as models for extreme values in many areas.The aim of this dissertation is to create new modifications of univariate extreme value models.The modifications developed in this dissertation are divided into two parts: in the first part, we make generalisations of GEV and GP, referred to as the Kumaraswamy GEV and Kumaraswamy GP distributions. The major benefit of these models is their ability to fit the skewed data better than other models. The other idea in this study comes from Chen, which is presented in Proceedings of the International Conference on Computational Intelligence and Software Engineering, pp. 1-4. However, the cumulative and probability density functions for this distribution do not appear to be valid functions. The correction of this model is presented in chapter 6.The major problem in extreme event models is the ability of the model to fit tails of data. In chapter 7, the idea of the Chen model with the correction is combined with the GEV distribution to introduce a new model for extreme values referred to as new extreme value (NEV) distribution. It seems to be more flexible than the GEV distribution.
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Feng, Jingyu. "Modeling Distributions of Test Scores with Mixtures of Beta Distributions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd1068.pdf.
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Lynch, O'Neil. "Mixture distributions with application to microarray data analysis." Scholar Commons, 2009. http://scholarcommons.usf.edu/etd/2075.
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The main goal in analyzing microarray data is to determine the genes that are differentially expressed across two types of tissue samples or samples obtained under two experimental conditions. In this dissertation we proposed two methods to determine differentially expressed genes. For the penalized normal mixture model (PMMM) to determine genes that are differentially expressed, we penalized both the variance and the mixing proportion parameters simultaneously. The variance parameter was penalized so that the log-likelihood will be bounded, while the mixing proportion parameter was penalized so that its estimates are not on the boundary of its parametric space. The null distribution of the likelihood ratio test statistic (LRTS) was simulated so that we could perform a hypothesis test for the number of components of the penalized normal mixture model. In addition to simulating the null distribution of the LRTS for the penalized normal mixture model, we showed that the maximum likelihood estimates were asymptotically normal, which is a first step that is necessary to prove the asymptotic null distribution of the LRTS. This result is a significant contribution to field of normal mixture model.
The modified p-value approach for detecting differentially expressed genes was also discussed in this dissertation. The modified p-value approach was implemented so that a hypothesis test for the number of components can be conducted by using the modified likelihood ratio test. In the modified p-value approach we penalized the mixing proportion so that the estimates of the mixing proportion are not on the boundary of its parametric space. The null distribution of the (LRTS) was simulated so that the number of components of the uniform beta mixture model can be determined. Finally, for both modified methods, the penalized normal mixture model and the modified p-value approach were applied to simulated and real data.
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Stewart, Michael Ian. "Asymptotic methods for tests of homogeneity for finite mixture models." University of Sydney. Mathematics and Statistics, 2002. http://hdl.handle.net/2123/855.
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We present limit theory for tests of homogeneity for finite mixture models. More specifically, we derive the asymptotic distribution of certain random quantities used for testing that a mixture of two distributions is in fact just a single distribution. Our methods apply to cases where the mixture component distributions come from one of a wide class of one-parameter exponential families, both continous and discrete. We consider two random quantities, one related to testing simple hypotheses, the other composite hypotheses. For simple hypotheses we consider the maximum of the standardised score process, which is itself a test statistic. For composite hypotheses we consider the maximum of the efficient score process, which is itself not a statistic (it depends on the unknown true distribution) but is asymptotically equivalent to certain common test statistics in a certain sense. We show that we can approximate both quantities with the maximum of a certain Gaussian process depending on the sample size and the true distribution of the observations, which when suitably normalised has a limiting distribution of the Gumbel extreme value type. Although the limit theory is not practically useful for computing approximate p-values, we use Monte-Carlo simulations to show that another method suggested by the theory, involving using a Studentised version of the maximum-score statistic and simulating a Gaussian process to compute approximate p-values, is remarkably accurate and uses a fraction of the computing resources that a straight Monte-Carlo approximation would.
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Belmasrour, Rachid. "The Distribution of Cotton Fiber Length." ScholarWorks@UNO, 2010. http://scholarworks.uno.edu/td/1216.
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By testing a fiber beard, certain cotton fiber length parameters can be obtained rapidly. This is the method used by the High Volume Instrument (HVI). This study is aimed to explore the approaches and obtain the inference of length distributions of HVI beard sam- ples in order to develop new methods that can help us find the distribution of original fiber lengths and further improve HVI length measurements. At first, the mathematical functions were searched for describing three different types of length distributions related to the beard method as used in HVI: cotton fiber lengths of the original fiber population before picked by the HVI Fibrosampler, fiber lengths picked by HVI Fibrosampler, and fiber beard's pro-jecting portion that is actually scanned by HVI. Eight sets of cotton samples with a wide range of fiber lengths are selected and tested on the Advanced Fiber Information System (AFIS). The measured single fiber length data is used for finding the underlying theoreti-cal length distributions, and thus can be considered as the population distributions of the cotton samples. In addition, fiber length distributions by number and by weight are dis- cussed separately. In both cases a mixture of two Weibull distributions shows a good fit to their fiber length data. To confirm the findings, Kolmogorov-Smirnov goodness-of-fit tests were conducted. Furthermore, various length parameters such as Mean Length (ML) and Upper Half Mean Length (UHML) are compared between the original distribution from the experimental data and the fitted distributions. The results of these obtained fiber length distributions are discussed by using Partial Least Squares (PLS) regression, where the dis-tribution of the original fiber length from the distribution of the projected one is estimated.
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Stewart, Michael. "Asymptotic methods for tests of homogeneity for finite mixture models." Connect to full text, 2002. http://hdl.handle.net/2123/855.
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Thesis (Ph. D.)--University of Sydney, 2002.Title from title screen (viewed Apr. 28, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.
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Osei, Ebenezer. "FITTING A DISTRIBUTION TO CATASTROPHIC EVENT." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2431.
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Statistics is a branch of mathematics which is heavily employed in the area of Actuarial Mathematics. This thesis first reviews the importance of statistical distributions in the analysis of insurance problems and the applications of Statistics in the area of risk and insurance. The Normal, Log-normal, Pareto, Gamma, standard Beta, Frechet, Gumbel, Weibull, Poisson, binomial, and negative binomial distributions are looked at and the importance of these distributions in general insurance is also emphasized. A careful review of literature is to provide practitioners in the general insurance industry with statistical tools which are of immediate application in the industry. These tools include estimation methods and fit statistics popular in the insurance industry. Finally this thesis carries out the task of fitting statistical distributions to the flood loss data in the 50 States of the United States.
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Svensson, Ingrid. "Estimation of wood fibre length distributions from censored mixture data." Doctoral thesis, Umeå : Department of Mathematics and Mathematical Statistics, Umeå Univ, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1094.
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Medasani, Swarup. "Robust algorithms for mixture decomposition with application to classification, boundary description, and image retrieval /." free to MU campus, to others for purchase, 1998. http://wwwlib.umi.com/cr/mo/fullcit?p9904860.
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Thogmartin, Wayne E., Jay E. Diffendorfer, Laura López-Hoffman, Karen Oberhauser, John Pleasants, Brice X. Semmens, Darius Semmens, Orley R. Taylor, and Ruscena Wiederholt. "Density estimates of monarch butterflies overwintering in central Mexico." PEERJ INC, 2017. http://hdl.handle.net/10150/624050.
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Given the rapid population decline and recent petition for listing of the monarch butterfly (Danaus plexippus L.) under the Endangered Species Act, an accurate estimate of the Eastern, migratory population size is needed. Because of difficulty in counting individual monarchs, the number of hectares occupied by monarchs in the overwintering area is commonly used as a proxy for population size, which is then multiplied by the density of individuals per hectare to estimate population size. There is, however, considerable variation in published estimates of overwintering density, ranging from 6.9-60.9 million ha(-1). We develop a probability distribution for overwinter density of monarch butterflies from six published density estimates. The mean density among the mixture of the six published estimates was similar to 27.9 million butterflies ha(-1) (95% CI [2.4-80.7] million ha(-1)); the mixture distribution is approximately log-normal, and as such is better represented by the median (21.1 million butterflies ha(-1)). Based upon assumptions regarding the number of milkweed needed to support monarchs, the amount of milkweed (Asciepias spp.) lost (0.86 billion stems) in the northern US plus the amount of milkweed remaining (1.34 billion stems), we estimate >1.8 billion stems is needed to return monarchs to an average population size of 6 ha. Considerable uncertainty exists in this required amount of milkweed because of the considerable uncertainty occurring in overwinter density estimates. Nevertheless, the estimate is on the same order as other published estimates, The studies included in our synthesis differ substantially by year, location, method, and measures of precision. A better understanding of the factors influencing overwintering density across space and time would be valuable for increasing the precision of conservation recommendations.
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直哉, 神野. "Studies on the capillary chromatography based on the tube radial distribution of aqueous-organic mixture carrier solvents under laminar flow conditions." Thesis, https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB12222842/?lang=0, 2011. https://doors.doshisha.ac.jp/opac/opac_link/bibid/BB12222842/?lang=0.
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Brown, Eric C. "Estimates of statistical power and accuracy for latent trajectory class enumeration in the growth mixture model." [Tampa, Fla.] : University of South Florida, 2003. http://purl.fcla.edu/fcla/etd/SFE0000622.
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Pavelka, Roman. "Využití kvantilových funkcí při kostrukci pravděpodobnostních modelů mzdových rozdělení." Doctoral thesis, Vysoká škola ekonomická v Praze, 2004. http://www.nusl.cz/ntk/nusl-77099.
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Over the course of years from 1995 to 2008 was acquired by Average Earnings Information System under the professional gestation of the Czech Republic Ministry of Labor and Social Affairs wage and personal data by individual employees. Thanks to the fact that in this statistical survey are collected wage and personal data by concrete employed persons it is possible to obtain a wage distribution, so it how this wages spread out among individual employees. Values that wages can be assumed in whole wage interval are not deterministical but they result from interactions of many random influences. The wage is necessary due to this randomness considered as random quantity with its probability density function. This spreading of wages in all labor market segments is described a wage distribution. Even though a representation of a high-income employee category is evidently small, one's incomes markedly affect statistically itemized average wage level and particularly the whole wage file variability. So wage employee collections are distinguished by the averaged wage that exceeds wages of a major employee mass and the high variability due to great wage heterogeneity. A general approach to distribution of earning modeling under current heterogeneity conditions don't permit to fit by some chosen distribution function or probably density function. This leads to the idea to apply some quantile approach with statistical modeling, i.e. to model an earning distribution with some appropriate inverse distributional function. The probability modeling by generalized or compound forms of quantile functions enables better to characterize a wage distribution, which distinguishes by high asymmetry and wage heterogeneity. The application of inverse distributional function as a probability model of a wage distribution can be expressed in forms of distributional mixture of partial employee's groups. All of the component distributions of this mixture model correspond to an employee's group with greater homogeneity of earnings. The partial employee's subfiles differ in parameters of their component density and in shares of this density in the total wage distribution of the wage file.
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Paz, Rosineide Fernando da. "Alternative regression models to beta distribution under bayesian approach." Universidade Federal de São Carlos, 2017. https://repositorio.ufscar.br/handle/ufscar/9146.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
The Beta distribution is a bounded domain distribution which has dominated the modeling the distribution of random variable that assume value between 0 and 1. Bounded domain distributions arising in various situations such as rates, proportions and index. Motivated by an analysis of electoral votes percentages (where a distribution with support on the positive real numbers was used, although a distribution with limited support could be more suitable) we focus on alternative distributions to Beta distribution with emphasis in regression models. In this work, initially we present the Simplex mixture model as a flexible model to modeling the distribution of bounded random variable then we extend the model to the context of regression models with the inclusion of covariates. The parameters estimation is discussed for both models considering Bayesian inference. We apply these models to simulated data sets in order to investigate the performance of the estimators. The results obtained were satisfactory for all the cases investigated. Finally, we introduce a parameterization of the L-Logistic distribution to be used in the context of regression models and we extend it to a mixture of mixed models.
A distribuição beta é uma distribuição com suporte limitado que tem dominado a modelagem de variáveis aleatórias que assumem valores entre 0 e 1. Distribuições com suporte limitado surgem em várias situações como em taxas, proporções e índices. Motivados por uma análise de porcentagens de votos eleitorais, em que foi assumida uma distribuição com suporte nos números reais positivos quando uma distribuição com suporte limitado seira mais apropriada, focamos em modelos alternativos a distribuição beta com enfase em modelos de regressão. Neste trabalho, apresentamos, inicialmente, um modelo de mistura de distribuições Simplex como um modelo flexível para modelar a distribuição de variáveis aleatórias que assumem valores em um intervalo limitado, em seguida estendemos o modelo para o contexto de modelos de regressão com a inclusão de covariáveis. A estimação dos parâmetros foi discutida para ambos os modelos, considerando o método bayesiano. Aplicamos os dois modelos a dados simulados para investigarmos a performance dos estimadores usados. Os resultados obtidos foram satisfatórios para todos os casos investigados. Finalmente, introduzimos a distribuição L-Logistica no contexto de modelos de regressão e posteriormente estendemos este modelo para o contexto de misturas de modelos de regressão mista.
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Nguyen, Minh Ha Information Technology & Electrical Engineering Australian Defence Force Academy UNSW. "Cooperative coevolutionary mixture of experts : a neuro ensemble approach for automatic decomposition of classification problems." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Information Technology and Electrical Engineering, 2006. http://handle.unsw.edu.au/1959.4/38752.
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Artificial neural networks have been widely used for machine learning and optimization. A neuro ensemble is a collection of neural networks that works cooperatively on a problem. In the literature, it has been shown that by combining several neural networks, the generalization of the overall system could be enhanced over the separate generalization ability of the individuals. Evolutionary computation can be used to search for a suitable architecture and weights for neural networks. When evolutionary computation is used to evolve a neuro ensemble, it is usually known as evolutionary neuro ensemble. In most real-world problems, we either know little about these problems or the problems are too complex to have a clear vision on how to decompose them by hand. Thus, it is usually desirable to have a method to automatically decompose a complex problem into a set of overlapping or non-overlapping sub-problems and assign one or more specialists (i.e. experts, learning machines) to each of these sub-problems. An important feature of neuro ensemble is automatic problem decomposition. Some neuro ensemble methods are able to generate networks, where each individual network is specialized on a unique sub-task such as mapping a subspace of the feature space. In real world problems, this is usually an important feature for a number of reasons including: (1) it provides an understanding of the decomposition nature of a problem; (2) if a problem changes, one can replace the network associated with the sub-space where the change occurs without affecting the overall ensemble; (3) if one network fails, the rest of the ensemble can still function in their sub-spaces; (4) if one learn the structure of one problem, it can potentially be transferred to other similar problems. In this thesis, I focus on classification problems and present a systematic study of a novel evolutionary neuro ensemble approach which I call cooperative coevolutionary mixture of experts (CCME). Cooperative coevolution (CC) is a branch of evolutionary computation where individuals in different populations cooperate to solve a problem and their fitness function is calculated based on their reciprocal interaction. The mixture of expert model (ME) is a neuro ensemble approach which can generate networks that are specialized on different sub-spaces in the feature space. By combining CC and ME, I have a powerful framework whereby it is able to automatically form the experts and train each of them. I show that the CCME method produces competitive results in terms of generalization ability without increasing the computational cost when compared to traditional training approaches. I also propose two different mechanisms for visualizing the resultant decomposition in high-dimensional feature spaces. The first mechanism is a simple one where data are grouped based on the specialization of each expert and a color-map of the data records is visualized. The second mechanism relies on principal component analysis to project the feature space onto lower dimensions, whereby decision boundaries generated by each expert are visualized through convex approximations. I also investigate the regularization effect of learning by forgetting on the proposed CCME. I show that learning by forgetting helps CCME to generate neuro ensembles of low structural complexity while maintaining their generalization abilities. Overall, the thesis presents an evolutionary neuro ensemble method whereby (1) the generated ensemble generalizes well; (2) it is able to automatically decompose the classification problem; and (3) it generates networks with small architectures.
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Silva, Renato Rodrigues. "A distribuição generalizada de Pareto e mistura de distribuições de Gumbel no estudo da vazão e da velocidade máxima do vento em Piracicaba, SP." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-18112008-145737/.
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A teoria dos valores extremos é um tópico da probabilidade que descreve a distribuição assintótica das estatísticas de ordem, tais como máximos ou mínimos, de uma seqüência de variáveis aleatórias que seguem uma função de distribuição F normalmente desconhecida. Descreve, ainda, a distribuição assintótica dos excessos acima de um valor limiar de um ou mais termos dessa seqüência. Dessa forma, as metodologias padrões utilizada neste contexto consistem no ajuste da distribuição generalizada dos valores extremos a uma série de máximos anuais ou no ajuste da distribuição generalizada de Pareto a uma série de dados compostas somente de observações excedentes de um valor limiar. No entanto, segundo Coles et al. (2003), há uma crescente insatisfação com o desempenho destes modelos padrões para predição de eventos extremos causada, possivelmente, por pressuposições não atendidas como a de independência das observações ou pelo fato de que os mesmos não sejam recomendados para serem utilizados em algumas situações específicas como por exemplo e quando observações de máximos anuais compostas por duas ou mais populações independentes de eventos extremos sendo que a primeira descreve eventos menos freqüentes e de maior magnitude e a segunda descreve eventos mais freqüentes e de menor magnitude. Então, os dois artigos que compõem este trabalho tem como objetivo apresentar alternativas de análise de valores extremos para estas situações em que o ajuste dos modelos padrões não são adequados. No primeiro, foram ajustadas as distribuições generalizada de Pareto e exponencial, caso particular da GP, aos dados de vazão média diária do Posto de Artemis, Piracicaba, SP, Brasil, conjuntamente com a técnica do desagrupamento, (declustering), e comparadas as estimativas dos níveis de retorno para períodos de 5, 10, 50 e 100 anos. Conclui-se que as estimativas intervalares dos níveis de retorno obtidas por meio do ajuste da distribuição exponencial são mais precisas do que as obtidas com o ajuste da distribuição generalizada de Pareto. No segundo artigo, por sua vez, foi apresentada uma metodologia para o ajuste da distribuição de Gumbel e de misturas de duas distribuições de Gumbel aos dados de velocidades de ventos mensais de Piracicaba, SP. Selecionou-se a distribuição que melhor ajustou-se aos dados por meio de testes de hipóteses bootstrap paramétrico e critérios de seleção AIC e BIC. E concluiu-se que a mistura de duas distribuições de Gumbel é a distribuição que melhor se ajustou-se aos dados de velocidades máxima de ventos dos meses de abril e maio, enquanto que o ajuste da distribuição de Gumbel foi o melhor para os meses de agosto e setembro.The extreme value theory is a probability topics that describes the asymtoptic distribution of order statistics such as maximum or minimum of random variables sequence that follow a distribution function F normaly unknown. Describes still, the excess asymtoptic distribution over threshold of this sequence. So, the standard methodologies of extremes values analysis are the fitting of generalized extreme value distribution to yearly maximum series or the fitting of generalized Pareto distribution to partial duration series. However, according to Coles et al. (2003), there is a growing dissatisfaction with the use this standard models for the prediction of extremes events and one of possible causes this fact may be a false assumptions about a sequence of observed data as a independence assumptions or because the standards models must not used in some specific situations like for example when maximum sample arise from two or more independents populations, where the first population describes more frequents and low intense events and the second population describes less frequents and more intense events. In this way, the two articles this work has a objective show alternatives about extreme values analysis for this situations that the standards models doesn´t recommended. In the first article, the generalized distribution Pareto and exponencial distribution, particular case of GP, together with to declustering methods was applied to mean daily flow of the Piracicaba river, Artemis station, Piracicaba, SP, and the estimates the return levels of 5, 10, 50 and 100 years were compared. We conclude that the interval estimates of the 50 and 100 year return levels obtained using the fitting the exponencial distribution are more precise than those obtained using the generalized Pareto distribution. In the second article, we propose the fit of Gumbel distribution and the Gumbel mixture to data maximum speed wind in Piracicaba, SP. We select the best model using bootstrap test of hypotheses and the AIC and BIC selection criteria We conclude that the mixture Gumbel is the best model to analyze the maximum wind speed data for months of april e may and otherside the fit of Gumbel distributions was the best fit to months of august e september.
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MARINHO, Pedro Rafael Diniz. "Some new families of continuos distributions." Universidade Federal de Pernambuco, 2016. https://repositorio.ufpe.br/handle/123456789/18862.
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FACEPE
The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean the life itself of a person, the operating time of equipment until its failure, the time of survival of a patient with a severe disease from the diagnosis, the duration of a social event as a marriage, among other meanings. The time of life or survival time is a positive continuous random variable, which can have constant, monotonic increasing, monotonic decreasing or non-monotonic (for example, in the form of a U) hazard function. In the last decades, several families of probabilistic models have been proposed. These models can be constructed based on some transformation of a parent distribution, commonly already known in the literature. A given linear combination or mixture of G models usually defines a class of probabilistic models having G as a special case. This thesis is composed of independent chapters. The first and last chapters are short chapters that include the introduction and conclusions of the study developed. Two families of distributions, namely the exponentiated logarithmic generated (ELG) class and the geometric Nadarajah-Haghighi (NHG) class are studied. The last one is a composition of the Nadarajah-Haghighi and geometric distributions. Further, we develop a statistical library for the R programming language called the AdequacyModel. This is an improvement of the package that was available on CRAN (Comprehensive R Archive Network) and it is currently in version 2.0.0. The two main functions of the library are the goodness.fit and pso functions. The first function allows to obtain the maximum likelihood estimates (MLEs) of the model parameters and some goodness-of-fit of the fitted probabilistic models. It is possible to choose the method of optimization for maximizing the log-likelihood function. The second function presents the method meta-heuristics global search known as particle swarm optimization (PSO) proposed by Eberhart and Kennedy (1995). Such methodology can be used for obtaining the MLEs necessary for the calculation of some measures of adequacy of the probabilistic models.
A área de análise de sobrevivência é importante na Estatística e é comumente aplicada às ciências biológicas, engenharias, ciências sociais, entre outras. Tipicamente, o tempo de vida ou falha pode ter diferentes interpretações dependendo da área de aplicação. Por exemplo, o tempo de vida pode significar a própria vida de uma pessoa, o tempo de funcionamento de um equipamento até sua falha, o tempo de sobrevivência de um paciente com uma doença grave desde o diagnóstico, a duração de um evento social como um casamento, entre outros significados. O tempo de vida é uma variável aleatória não negativa, que pode ter a função de risco na forma constante, monótona crescente, monótona decrescente ou não monótona (por exemplo, em forma de U). Nas últimas décadas, várias famílias de modelos probabilísticos têm sido propostas. Esses modelos podem ser construídos com base em alguma transformação de uma distribuição padrão, geralmente já conhecida na literatura. Uma dada combinação linear ou mistura de modelos G normalmente define uma classe de modelos probabilísticos tendo G como caso especial. Esta tese é composta de capítulos independentes. O primeiro e último são curtos capítulos que incluem a introdução e as conclusões do estudo desenvolvido. Duas famílias de distribuições, denominadas de classe “exponentiated logarithmic generated” (ELG) e a classe “geometric Nadarajah-Haghighi” (NHG) s˜ao estudadas. A ´ultima ´e uma composi¸c˜ao das distribuições de Nadarajah-Haghighi e geométrica. Além disso, desenvolvemos uma biblioteca estatística para a linguagem de programação R chamada AdequacyModel. Esta é uma melhoria do pacote que foi disponibilizado no CRAN (Comprehensive R Archive Network) e está atualmente na versão 2.0.0. As duas principais funções da biblioteca são as funções goodness.fit e pso. A primeira função permite obter as estimativas de máxima verossimilhança (EMVs) dos parâmetros de um modelo e algumas medidas de bondade de ajuste dos modelos probabilísticos ajustados. E possível escolher o método de otimização para maximizar a função de log-verossimilhan¸ca. A segunda função apresenta o método meta-heurístico de busca global conhecido como Particle Swarm Optimization (PSO) proposto por Eberhart e Kennedy (1995). Algumas metodologias podem ser utilizadas para obtenção das EMVs necessárias para o cálculo de algumas medidas de adequação dos modelos probablísticos ajustados.
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Engberg, Alexander. "An empirical comparison of extreme value modelling procedures for the estimation of high quantiles." Thesis, Uppsala universitet, Statistiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-297063.
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The peaks over threshold (POT) method provides an attractive framework for estimating the risk of extreme events such as severe storms or large insurance claims. However, the conventional POT procedure, where the threshold excesses are modelled by a generalized Pareto distribution, suffers from small samples and subjective threshold selection. In recent years, two alternative approaches have been proposed in the form of mixture models that estimate the threshold and a folding procedure that generates larger tail samples. In this paper the empirical performances of the conventional POT procedure, the folding procedure and a mixture model are compared by modelling data sets on fire insurance claims and hurricane damage costs. The results show that the folding procedure gives smaller standard errors of the parameter estimates and in some cases more stable quantile estimates than the conventional POT procedure. The mixture model estimates are dependent on the starting values in the numerical maximum likelihood estimation, and are therefore difficult to compare with those from the other procedures. The conclusion is that none of the procedures is overall better than the others but that there are situations where one method may be preferred.
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Rocha, Ricardo Ferreira da. "Defective models for cure rate modeling." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7751.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Modeling of a cure fraction, also known as long-term survivors, is a part of survival analysis. It studies cases where supposedly there are observations not susceptible to the event of interest. Such cases require special theoretical treatment, in a way that the modeling assumes the existence of such observations. We need to use some strategy to make the survival function converge to a value p 2 (0; 1), representing the cure rate. A way to model cure rates is to use defective distributions. These distributions are characterized by having probability density functions which integrate to values less than one when the domain of some of their parameters is di erent from that usually de ned. There is not so much literature about these distributions. There are at least two distributions in the literature that can be used for defective modeling: the Gompertz and inverse Gaussian distribution. The defective models have the advantage of not need the assumption of the presence of immune individuals in the data set. In order to use the defective distributions theory in a competitive way, we need a larger variety of these distributions. Therefore, the main objective of this work is to increase the number of defective distributions that can be used in the cure rate modeling. We investigate how to extend baseline models using some family of distributions. In addition, we derive a property of the Marshall-Olkin family of distributions that allows one to generate new defective models.
A modelagem da fração de cura e uma parte importante da an álise de sobrevivência. Essa área estuda os casos em que, supostamente, existem observa ções não suscetíveis ao evento de interesse. Tais casos requerem um tratamento teórico especial, de forma que a modelagem pressuponha a existência de tais observações. E necessário usar alguma estratégia para tornar a função de sobrevivência convergente para um valor p 2 (0; 1), que represente a taxa de cura. Uma forma de modelar tais frações e por meio de distribui ções defeituosas. Essas distribuições são caracterizadas por possuirem funções de densidade de probabilidade que integram em valores inferiores a um quando o domínio de alguns dos seus parâmetros e diferente daquele em que e usualmente definido. Existem, pelo menos, duas distribuições defeituosas na literatura: a Gompertz e a inversa Gaussiana. Os modelos defeituosos têm a vantagem de não precisar pressupor a presença de indivíduos imunes no conjunto de dados. Para utilizar a teoria de d istribuições defeituosas de forma competitiva e necessário uma maior variedade dessas distribuições. Portanto, o principal objetivo deste trabalho e aumentar o n úmero de distribuições defeituosas que podem ser utilizadas na modelagem de frações de curas. Nós investigamos como estender os modelos defeituosos básicos utilizando certas famílias de distribuições. Além disso, derivamos uma propriedade da famí lia Marshall-Olkin de distribuições que permite gerar uma nova classe de modelos defeituosos.
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Gurkan, Gulsah. "From OLS to Multilevel Multidimensional Mixture IRT: A Model Refinement Approach to Investigating Patterns of Relationships in PISA 2012 Data." Thesis, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109191.
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Thesis advisor: Henry I. BraunSecondary analyses of international large-scale assessments (ILSA) commonly characterize relationships between variables of interest using correlations. However, the accuracy of correlation estimates is impaired by artefacts such as measurement error and clustering. Despite advancements in methodology, conventional correlation estimates or statistical models not addressing this problem are still commonly used when analyzing ILSA data. This dissertation examines the impact of both the clustered nature of the data and heterogeneous measurement error on the correlations reported between background data and proficiency scales across countries participating in ILSA. In this regard, the operating characteristics of competing modeling techniques are explored by means of applications to data from PISA 2012. Specifically, the estimates of correlations between math self-efficacy and math achievement across countries are the principal focus of this study. Sequentially employing four different statistical techniques, a step-wise model refinement approach is used. After each step, the changes in the within-country correlation estimates are examined in relation to (i) the heterogeneity of distributions, (ii) the amount of measurement error, (iii) the degree of clustering, and (iv) country-level math performance. The results show that correlation estimates gathered from two-dimensional IRT models are more similar across countries in comparison to conventional and multilevel linear modeling estimates. The strength of the relationship between math proficiency and math self-efficacy is moderated by country mean math proficiency and this was found to be consistent across all four models even when measurement error and clustering were taken into account. Multilevel multidimensional mixture IRT modeling results support the hypothesis that low-performing groups within countries have a lower correlation between math self-efficacy and math proficiency. A weaker association between math self-efficacy and math proficiency in lower achieving groups is consistently seen across countries. A multilevel mixture IRT modeling approach sheds light on how this pattern emerges from greater randomness in the responses of lower performing groups. The findings from this study demonstrate that advanced modeling techniques not only are more appropriate given the characteristics of the data, but also provide greater insight about the patterns of relationships across countries
Thesis (PhD) — Boston College, 2021
Submitted to: Boston College. Lynch School of Education
Discipline: Educational Research, Measurement and Evaluation
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Janeiro, Vanderly. "Modelagem de dados contínuos censurados, inflacionados de zeros." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-20092010-090511/.
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Muitos equipamentos utilizados para quantificar substâncias, como toxinas em alimentos, freqüentemente apresentam deficiências para quantificar quantidades baixas. Em tais casos, geralmente indicam a ausência da substância quando esta existe, mas está abaixo de um valor pequeno \'ksi\' predeterminado, produzindo valores iguais a zero não necessariamente verdadeiros. Em outros casos, detectam a presença da substância, mas são incapazes de quantificá-la quando a quantidade da substância está entre \'ksai\' e um valor limiar \'tau\', conhecidos. Por outro lado, quantidades acima desse valor limiar são quantificadas de forma contínua, dando origem a uma variável aleatória contínua X cujo domínio pode ser escrito como a união dos intervalos, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] e (\'tau\', ?), sendo comum o excesso de valores iguais a zero. Neste trabalho, são propostos modelos que possibilitam discriminar a probabilidade de zeros verdadeiros, como o modelo de mistura com dois componentes, sendo um degenerado em zero e outro com distribuição contínua, sendo aqui consideradas as distribuições: exponencial, de Weibull e gama. Em seguida, para cada modelo, foram observadas suas características, propostos procedimentos para estimação de seus parâmetros e avaliados seus potenciais de ajuste por meio de métodos de simulação. Finalmente, a metodologia desenvolvida foi ilustrada por meio da modelagem de medidas de contaminação com aflatoxina B1, observadas em grãos de milho, de três subamostras de um lote de milho, analisados no Laboratório de Micotoxinas do Departamento de Agroindústria, Alimentos e Nutrição da ESALQ/USP. Como conclusões, na maioria dos casos, as simulações indicaram eficiência dos métodos propostos para as estimações dos parâmetros dos modelos, principalmente para a estimativa do parâmetro \'delta\' e do valor esperado, \'Epsilon\' (Y). A modelagem das medidas de aflatoxina, por sua vez, mostrou que os modelos propostos são adequados aos dados reais, sendo que o modelo de mistura com distribuição de Weibull, entretanto, ajustou-se melhor aos dados.Much equipment used to quantify substances, such as toxins in foods, is unable to measure low amounts. In cases where the substance exists, but in an amount below a small fixed value \'ksi\' , the equipment usually indicates that the substance is not present, producing values equal to zero. In cases where the quantity is between \'\'ksi\' and a known threshold value \'tau\', it detects the presence of the substance but is unable to measure the amount. When the substance exists in amounts above the threshold value ?, it is measure continuously, giving rise to a continuous random variable X whose domain can be written as the union of intervals, [ómicron, \"ksai\'), [\"ksai\', \'tau\' ] and (\'tau\', ?), This random variable commonly has an excess of zero values. In this work we propose models that can detect the probability of true zero, such as the mixture model with two components, one being degenerate at zero and the other with continuous distribution, where we considered the distributions: exponential, Weibull and gamma. Then, for each model, its characteristics were observed, procedures for estimating its parameters were proposed and its potential for adjustment by simulation methods was evaluated. Finally, the methodology was illustrated by modeling measures of contamination with aflatoxin B1, detected in grains of corn from three sub-samples of a batch of corn analyzed at the laboratory of of Mycotoxins, Department of Agribusiness, Food and Nutrition ESALQ/USP. In conclusion, in the majority of cases the simulations indicated that the proposed methods are efficient in estimating the parameters of the models, in particular for estimating the parameter ? and the expected value, E(Y). The modeling of measures of aflatoxin, in turn, showed that the proposed models are appropriate for the actual data, however the mixture model with a Weibull distribution fits the data best.
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Duarte, Agostinho Domingos Caholo. "Distribution and mixture of Cape and Cunene horse mackerel, Tachurus capensis and Tracherus trecae in the Angola-Benguela front in relation to environmental and other factors." Master's thesis, University of Cape Town, 2001. http://hdl.handle.net/11427/6253.
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Bibliography: leaves 128-133.This thesis makses an analysis of survey data of horse mackerel catch per unit effort and acoustics data from R/V Dr. Fridtjof Nansen over twelve years in the region of the Angola-Benguela front. The main objectives are: to characterize the pattern of distribution and mixture of Cunene and Cape horse mackerel in the area around the Angola-Benguela front and to study the relationships between the distribution of T. capensis and T. trecae and the movements of the Angola-Benguela front. The role of sea surface temperature (SST) was also examined, assuming that this environmental parameter would be related to the seasonal variation in distribution of both species of horse mackerel, at least in the overlap area.
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Koladjo, Babagnidé François. "Estimation non paramétrique du nombre d'espèces : Application à l'étude de la faune ichtyologique du bassin du fleuve Ouëmé." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112153.
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Ce manuscrit est structuré en deux parties. La première partie composée des chapitres 2à 4 aborde le problème d'estimation du nombre de classes dans une population avec une application en écologie. La deuxième partie, correspondant au chapitre 5,concerne la mise en oeuvre de méthodes statistiques pour analyser des données de pêche. Dans la première partie, nous considérons une population hétérogène subdiviséeen plusieurs classes. À partir d'un échantillon, les effectifs d'individus observés parclasse, encore appelés abondances, sont utilisés pour estimer le nombre total declasses dans la population. Dans la littérature consacrée à l'estimation du nombrede classes, les méthodes basées sur un mélange de distributions de Poisson semblentêtre les plus performantes (voir par exemple les travaux de Chao and Bunge (2002)dans le cadre paramétrique et celui de Wang and Lindsay (2005) dans un cadrenon paramétrique). La mise en oeuvre de ces approches sur des données réellesmet en évidence que la distribution des abondances peut être approchée par unedistribution convexe. Nous proposons une approche non paramétrique pour estimerla distribution des abondances sous contrainte de convexité. Cette contrainte définitun cadre théorique d'estimation d'une densité discrète. Le problème d'estimation dunombre de classes est donc abordé en deux volets. Nous montrons d'une part l'existenceet l'unicité d'un estimateur d'une densité discrète sous la contrainte de convexité.Sous cette contrainte, nous démontrons qu'une densité discrète s'écrit comme un mélange de densités triangulaires. À partir de l'algorithme de réduction du supportproposé par Groeneboom et al. (2008), nous proposons un algorithme exact pourestimer les proportions dans le mélange. D'autre part, la procédure d'estimationd'une densité discrète convexe nous sert de cadre pour l'estimation de la distributiontronquée en zéro des observations d'abondance. L'estimation de la loi tronquée obtenue est ensuite prolongée en zéro pour estimer la probabilité qu'une classe ne soit pasobservée. Ce prolongement en zéro est fait de façon à annuler la proportion dela première composante dans le mélange de densités triangulaires. Nousaboutissons à une estimation du nombre de classes à l'aide d'un modèle binomial ensupposant que chaque classe apparaît dans un échantillon par une épreuve deBernoulli. Nous montrons la convergence en loi de l'estimateur proposé. Sur le plan pratique, une application aux données réelles en écologie est présentée. La méthode est ensuite comparée à d'autres méthodes concurrentes à l'aide de simulations. La seconde partie présente l'analyse des données de pêche collectées dans le fleuveOuémé au Bénin. Nous proposons une démarche statistique permettant de regrouperles espèces selon leur profil temporel d'abondances, d'estimer le stock d'une espèceainsi que leur capturabilité par les engins de pêche artisanaleThis manuscript is structured in two parts. The #rst part composed of Chapters 2to 4 deals with the problem of estimating the number of classes in a population withan application in ecology. The second part, corresponding to Chapter 5, concernsthe application of statistical methods to analyze fisheries data.In the first part, we consider a heterogeneous population split into several classes.From a sample, the numbers of observed individuals per class, also called abun-dances, are used to estimate the total number of classes in the population. In theliterature devoted to the number of classes estimation, methods based on a mix-ture of Poisson distributions seem to be the most effcient (see for example the workof Chao and Bunge (2002) in the parametric framework and that of Wang and Lind-say (2005) in a non-parametric framework). Applications of these approaches to realdata show that the distribution of abundances can be approximated by a convexdistribution. We propose a non-parametric approach to estimate the distribution ofabundances under the constraint of convexity. This constraint defines a theoreticalframework for estimating a discrete density. The problem of estimating the numberof classes is then tackled in two steps.We show on the one hand the existence and uniqueness of an estimator of adiscrete density under the constraint of convexity. Under this constraint, we provethat a discrete density can be written as a mixture of triangular distributions. Usingthe support reduction algorithm proposed by Groeneboom et al. (2008), we proposean exact algorithm to estimate the proportions in the mixture.On the other hand, the estimation procedure of a discrete convex density is usedto estimate the zero-truncated distribution of the observed abundance data. Thezero-truncated distribution estimate is then extended at zero to derive an estimateof the probability that a class is not observed. This extension is made so as tocancel the first component in the mixture of triangular distributions. An estimateof the total number of classes is obtained through a binomial model assuming thateach class appears in a sample by a Bernoulli trial. We show the convergence inlaw of the proposed estimator. On practical view, an application to real ecologicaldata is presented. The method is then compared to other concurrent methods usingsimulations.The second part presents the analysis of fisheries data collected on the Ouémériver in Benin. We propose a statistical approach for grouping species accordingto their temporal abundance profile, to estimate the stock of a species and theircatchability by artisanal fishing gears
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Malsiner-Walli, Gertraud, Sylvia Frühwirth-Schnatter, and Bettina Grün. "Model-based clustering based on sparse finite Gaussian mixtures." Springer, 2016. http://dx.doi.org/10.1007/s11222-014-9500-2.
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In the framework of Bayesian model-based clustering based on a finite mixture of Gaussian distributions, we present a joint approach to estimate the number of mixture components and identify cluster-relevant variables simultaneously as well as to obtain an identified model. Our approach consists in specifying sparse hierarchical priors on the mixture weights and component means. In a deliberately overfitting mixture model the sparse prior on the weights empties superfluous components during MCMC. A straightforward estimator for the true number of components is given by the most frequent number of non-empty components visited during MCMC sampling. Specifying a shrinkage prior, namely the normal gamma prior, on the component means leads to improved parameter estimates as well as identification of cluster-relevant variables. After estimating the mixture model using MCMC methods based on data augmentation and Gibbs sampling, an identified model is obtained by relabeling the MCMC output in the point process representation of the draws. This is performed using K-centroids cluster analysis based on the Mahalanobis distance. We evaluate our proposed strategy in a simulation setup with artificial data and by applying it to benchmark data sets. (authors' abstract)
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Farcas, Florentina Angela. "Evaluation of Asphalt Field Cores with Simple Performance Tester and X-ray Computed Tomography." Licentiate thesis, KTH, Väg- och banteknik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-91803.
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The importance of aggregate structure and air voids distribution for asphalt mixture rutting and cracking performance has been well established on the basis of experience and is well documented in the literature. Past and current investigations are limited to assessment of performance based on macroscopic behavior due to the difficulty associated with the quantitative measurement and analysis of the internal structure of asphalt mixtures. Lately, technical advances in X-ray Computed Tomography (CT) and image processing and analysis has made possible to bring the attention also to the internal structure of asphalt mixtures. SPT results from asphalt field cores, including dynamic modulus (before and after loading) and microstrain accumulation (flow number), exhibited significant variability; most likely, induced by irregularities in the core shape. The analysis of aggregate structure and air voids distribution performed trough X-ray CT, clearly identified segregation in the asphalt mixture as a key factor that induced variability in SPT results.QC 20120320
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Kavaliauskas, Mindaugas. "Daugiamačių Gauso skirstinių mišinio statistinė analizė, taikant duomenų projektavimą." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050121_131502-50982.
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Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.
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Kavaliauskas, Mindaugas. "Daugiamačiu Gauso skirstinių mišinio statistinė analizė, taikant duomenų projektavimą." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050121_133306-49239.
Full textAbstract:
Problem of the dissertation. The Gaussian random values are very common in practice, because if a random value depends on many additive factors, according to the Central Limit Theorem (if particular conditions are satisfied), the sum is approximately from Gaussian distribution. If the observed random value belongs to one of the several classes, it is from the Gaussian distribution mixture model. The mixtures of the Gaussian distributions are common in various fields: biology, medicine, astronomy, military science and many others. The most important statistical problems are problems of mixture identification and data clustering. In case of high data dimension, these tasks are not completely solved. The new parameter estimation of the multivariate Gaussian distribution mixture model and data clustering methods are proposed and analysed in the dissertation. Since it is much easier to solve these problems in univariate case, the projection-based approach is used. The aim of the dissertation. The aim of this work is the development of constructive algorithms for distribution analysis and clustering of data from the mixture model of the Gaussian distributions.
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Hornik, Kurt, and Bettina Grün. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions." American Statistical Association, 2014. http://epub.wu.ac.at/4893/1/v58i10.pdf.
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Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von
Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm
for maximum likelihood estimation. Special features are the possibility to use
sparse matrix representations for the input data, different variants of the expectationmaximization
algorithm, different methods for determining the concentration parameters
in the M-step and to impose constraints on the concentration parameters over the components.
In this paper we describe the main fitting function of the package and illustrate its
application. In addition we compare the clustering performance of finite mixtures of
von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of
several numerical issues which occur for estimating the concentration parameters and for
determining the normalizing constant of the von Mises-Fisher distribution. (authors' abstract)
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Pokorný, Pavel. "Aplikace zobecněného lineárního modelu na směsi pravděpodobnostních rozdělení." Master's thesis, Vysoká škola ekonomická v Praze, 2009. http://www.nusl.cz/ntk/nusl-17135.
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This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.
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Bai, Xiuqin. "Robust mixtures of regression models." Diss., Kansas State University, 2014. http://hdl.handle.net/2097/18683.
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Doctor of PhilosophyDepartment of Statistics
Kun Chen and Weixin Yao
This proposal contains two projects that are related to robust mixture models. In the robust project, we propose a new robust mixture of regression models (Bai et al., 2012). The existing methods for tting mixture regression models assume a normal distribution for error and then estimate the regression param- eters by the maximum likelihood estimate (MLE). In this project, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. In the second project, we propose a new robust mixture of linear mixed-effects models. The traditional mixture model with multiple linear mixed effects, assuming Gaussian distribution for random and error parts, is sensitive to outliers. We will propose a mixture of multiple linear mixed t-distributions to robustify the estimation procedure. An EM algorithm is provided to and the MLE under the assumption of t- distributions for error terms and random mixed effects. Furthermore, we propose to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. In the simulation study, we demonstrate that our proposed model works comparably to the traditional estimation method when there are no outliers and the errors and random mixed effects are normally distributed, but works much better if there are outliers or the distributions of the errors and random mixed effects have heavy tails.
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Percy, Edward Richard Jr. "Corrected LM goodness-of-fit tests with applicaton to stock returns." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1134416514.
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Yajima, Ayako. "Assessment of Soil Corrosion in Underground Pipelines via Statistical Inference." University of Akron / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=akron1435602696.
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