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Dissertations / Theses on the topic 'Probability Distributions Theory'
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Giamouridis, Daniel. "Implied probability distributions : estimation, testing and applications." Thesis, City University London, 2001. http://openaccess.city.ac.uk/8388/.
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A relatively large number of authors have proposed alternative techniques for the estimation of implied risk-neutral densities. As a general rule, an assumption for a theoretical equilibrium option pricing model is made and with the use of cross-sections of observed options prices point estimates of the risk-neutral probability densities are obtained. The present study is primarily concerned with the estimation of implied riskneutral densities by means of a semi-parametric Edgeworth Series Expansion probability model as an alternative to the widely criticized log-normal parameterization of the Black, Scholes and Merton model. Despite the relatively early introduction of this type of models in academic literature in the early '80s, it was not until the mid '90s that people started showing interest in their applications. Moreover, no studies by means of the Edgeworth Series Expansion probability model have so far been conducted with American style options. To this end, the present work initially develops the general theoretical framework and the numerical algorithm for the estimation of implied risk-neutral densities of the Edgeworth Series Expansion type from options prices. The technique is applicable to European options written on a generalized asset that pays dividends in continuous time or American futures options. The empirical part of the study considers data for the Oil and the Interest rates markets. The first task in the empirical investigation is to address general concerns with regard to the validity of an implied risk-neutral density estimation technique and its ability to stimulate meaningful discussion. To this end, the consistency of the Edgeworth Series Expansion type implied densities with the data is checked. This consistency is viewed in a broader sense: internal consistency - adequate fit to observed data - and economic rationale of the respective densities. An analysis is, therefore, performed to examine the properties of the implied densities in the presence of large changes in economic conditions. More specifically, the ability of the implied Edgeworth Series Expansion type implied densities to capture speculation over future eventualities and their capacity to immediately reflect changes in the market sentiment are examined. Motivated by existing concerns in the literature that the differences between the estimates from an alternative parameterization and the log-normal Black-Scholes-Merton parameterization may be apparent - better fit to observed data - but not significant.
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Anabila, Moses A. "Skew Pareto distributions." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453191.
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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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Ma, Kin-Keung. "Infinite prefix codes for geometric distributions /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20MA.
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Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2004.<br>Includes bibliographical references (leaves 74-76). Also available in electronic version. Access restricted to campus users.
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Merrell, Paul Clark. "Structure from Motion Using Optical Flow Probability Distributions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd764.pdf.
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Lai, Pik-ying, and 黎碧瑩. "Lp regression under general error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30287844.
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Wahed, Abdus S. "General families of skew-symmetric distributions." Virtual Press, 2000. http://liblink.bsu.edu/uhtbin/catkey/1178355.
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The family of univariate skew-normal probability distributions, an extension of symmetric normal distribution to a general case of asymmetry, was originally proposed by Azzalani [1]. Since its introduction, very limited research has been conducted in this area. An extension of the univariate skew-normal distribution to the multivariate case was considered by Azzalani and Dalla Valle [4]. Its application in statistics was recently considered by Azzalani and Capitanio [3]. As a general result, Azzalani (1985) [See [1]] showed that, any symmetric distribution can be viewed as a member of a more general class of skewed distributions.In this study we establish some properties of general family of skewed distributions. Examples of general family of asymmetric distributions is presented in a way to show their differences from the corresponding symmetric distributions. The skew-logistic distribution and its properties are considered in great details.<br>Department of Mathematical Sciences
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Majumder, M. Mahbubul A. "On Tukey's gh family of distributions." Virtual Press, 2007. http://liblink.bsu.edu/uhtbin/catkey/1371472.
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Skewness and elongation are two factors that directly determine the shape of a probability distribution. Thus, to obtain a flexible distribution it is always desirable that the parameters of the distribution directly determine the skewness and elongation. To meet this purpose, Tukey (1977) introduced a family of distributions called g-and-h family (gh family) based on a transformation of the standard normal variable where g and h determine the skewness and the elongation, respectively. The gh family of distributions was extensively studied by Hoaglin (1985) and Martinez and Iglewicz (1984). For its flexibility in shape He and Raghunathan (2006) have used this distribution for multiple imputations. Because of the complex nature of this family of distributions, it is not possible to have an explicit mathematical form of the density function and the estimates of the parameters g and h fully depend on extensive numerical computations.In this study, we have developed algorithms to numerically compute the density functions. We present algorithms to obtain the estimates of g and h using method of moments, quantile method and maximum likelihood method. We analyze the performance of each method and compare them using simulation technique. Finally, we study some special cases of gh family and their properties.<br>Department of Mathematical Sciences
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Millar, R. B. "Estimation of mixing and mixed distributions /." Thesis, Connect to this title online; UW restricted, 1989. http://hdl.handle.net/1773/8984.
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Ding, Xiqian, and 丁茜茜. "Some new statistical methods for a class of zero-truncated discrete distributions with applications." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2015. http://hdl.handle.net/10722/211126.
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Counting data without zero category often occur in various _elds. Examples include days of hospital stay for patients, numbers of publication for tenure-tracked faculty in a university, numbers of tra_c violation for drivers during a certain period and so on. A class of zero-truncated discrete models such as zero-truncated Poisson, zero-truncated binomial and zero-truncated negative-binomial distributions are proposed in literature to model such count data. In this thesis, firstly, literature review is presented in Chapter 1 on a class of commonly used univariate zero-truncated discrete distributions.
In Chapter 2, a unified method is proposed to derive the distribution of the sum of i.i.d. zero-truncated distribution random variables, which has important applications in the construction of the shortest Clopper-Person confidence intervals of parameters of interest and in the calculation of the exact p-value of a two-sided test for small sample sizes in one sample problem. These problems are discussed in Section 2.4. Then a novel expectation-maximization (EM) algorithm is developed for calculating the maximum likelihood estimates (MLEs) of parameters in general zero-truncated discrete distributions. An important feature of the proposed EM algorithm is that the latent variables and the observed variables are independent, which is unusual in general EM-type algorithms. In addition, a unified minorization-maximization (MM) algorithm for obtaining the MLEs of parameters in a class of zero-truncated discrete distributions is provided.
The first objective of Chapter 3 is to propose the multivariate zero-truncated Charlier series (ZTCS) distribution by developing its important distributional properties, and providing efficient MLE methods via a novel data augmentation in the framework of the EM algorithm. Since the joint marginal distribution of any r-dimensional sub-vector of the multivariate ZTCS random vector of dimension m is an r-dimensional zero-deated Charlier series (ZDCS) distribution (1 6 r < m), it is the second objective of Chapter 3 to propose a new family of multivariate zero-adjusted Charlier series (ZACS) distributions (including the multivariate ZDCS distribution as a special member) with a more flexible correlation structure by accounting for both inflation and deflation at zero. The corresponding distributional properties are explored and the associated MLE method via EM algorithm is provided for analyzing correlated count data.<br>published_or_final_version<br>Statistics and Actuarial Science<br>Master<br>Master of Philosophy
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Sun, Yannan. "Extremal dependence of multivariate distributions and its applications." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Dissertations/Spring2010/Y_SUN_041610.pdf.
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陳冠全 and Koon-chuen Chen. "Invariant limiting shape distributions for some sequential rectangularmodels." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31238233.
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屠烈偉 and Lit-wai Tao. "Statistical inference on a mixture model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977480.
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Tao, Lit-wai. "Statistical inference on a mixture model." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13781479.
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Chen, Koon-chuen. "Invariant limiting shape distributions for some sequential rectangular models /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20998934.
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Sitton, David E. R. "Generating random absolutely continuous distributions." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/28989.
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Chan, Chun-man, and 陳俊文. "On a topic of Bayesian analysis using scale mixtures distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31223989.
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Chan, Chun-man. "On a topic of Bayesian analysis using scale mixtures distributions." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22665183.
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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.<br>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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Hao, Jie. "Some New Probability Distributions Based on Random Extrema and Permutation Patterns." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etd/2344.
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In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X1,X2, ..., XN, where each Xi has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where Xi is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for the continuous random variables such as Arcsine, Topp-Leone, and N is chosen to be Geometric or Zipf. Wherever appropriate, we estimate of the parameter in the one-parameter family in question and test the hypotheses about the parameter. In the last section, two permutation distributions are introduced and studied.
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Nilsson, Viktor. "Prediction of Dose Probability Distributions Using Mixture Density Networks." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-273610.
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In recent years, machine learning has become utilized in external radiation therapy treatment planning. This involves automatic generation of treatment plans based on CT-scans and other spatial information such as the location of tumors and organs. The utility lies in relieving clinical staff from the labor of manually or semi-manually creating such plans. Rather than predicting a deterministic plan, there is great value in modeling it stochastically, i.e. predicting a probability distribution of dose from CT-scans and delineated biological structures. The stochasticity inherent in the RT treatment problem stems from the fact that a range of different plans can be adequate for a patient. The particular distribution can be thought of as the prevalence in preferences among clinicians. Having more information about the range of possible plans represented in one model entails that there is more flexibility in forming a final plan. Additionally, the model will be able to reflect the potentially conflicting clinical trade-offs; these will occur as multimodal distributions of dose in areas where there is a high variance. At RaySearch, the current method for doing this uses probabilistic random forests, an augmentation of the classical random forest algorithm. A current direction of research is learning the probability distribution using deep learning. A novel parametric approach to this is letting a suitable deep neural network approximate the parameters of a Gaussian mixture model in each volume element. Such a neural network is known as a mixture density network. This thesis establishes theoretical results of artificial neural networks, mainly the universal approximation theorem, applied to the activation functions used in the thesis. It will then proceed to investigate the power of deep learning in predicting dose distributions, both deterministically and stochastically. The primary objective is to investigate the feasibility of mixture density networks for stochastic prediction. The research question is the following. U-nets and Mixture Density Networks will be combined to predict stochastic doses. Does there exist such a network, powerful enough to detect and model bimodality? The experiments and investigations performed in this thesis demonstrate that there is indeed such a network.<br>Under de senaste åren har maskininlärning börjat nyttjas i extern strålbehandlingsplanering. Detta involverar automatisk generering av behandlingsplaner baserade på datortomografibilder och annan rumslig information, såsom placering av tumörer och organ. Nyttan ligger i att avlasta klinisk personal från arbetet med manuellt eller halvmanuellt skapa sådana planer. I stället för att predicera en deterministisk plan finns det stort värde att modellera den stokastiskt, det vill säga predicera en sannolikhetsfördelning av dos utifrån datortomografibilder och konturerade biologiska strukturer. Stokasticiteten som förekommer i strålterapibehandlingsproblemet beror på att en rad olika planer kan vara adekvata för en patient. Den särskilda fördelningen kan betraktas som förekomsten av preferenser bland klinisk personal. Att ha mer information om utbudet av möjliga planer representerat i en modell innebär att det finns mer flexibilitet i utformningen av en slutlig plan. Dessutom kommer modellen att kunna återspegla de potentiellt motstridiga kliniska avvägningarna; dessa kommer påträffas som multimodala fördelningar av dosen i områden där det finns en hög varians. På RaySearch används en probabilistisk random forest för att skapa dessa fördelningar, denna metod är en utökning av den klassiska random forest-algoritmen. En aktuell forskningsriktning är att generera in sannolikhetsfördelningen med hjälp av djupinlärning. Ett oprövat parametriskt tillvägagångssätt för detta är att låta ett lämpligt djupt neuralt nätverk approximera parametrarna för en Gaussisk mixturmodell i varje volymelement. Ett sådant neuralt nätverk är känt som ett mixturdensitetsnätverk. Den här uppsatsen fastställer teoretiska resultat för artificiella neurala nätverk, främst det universella approximationsteoremet, tillämpat på de aktiveringsfunktioner som används i uppsatsen. Den fortsätter sedan att utforska styrkan av djupinlärning i att predicera dosfördelningar, både deterministiskt och stokastiskt. Det primära målet är att undersöka lämpligheten av mixturdensitetsnätverk för stokastisk prediktion. Forskningsfrågan är följande. U-nets och mixturdensitetsnätverk kommer att kombineras för att predicera stokastiska doser. Finns det ett sådant nätverk som är tillräckligt kraftfullt för att upptäcka och modellera bimodalitet? Experimenten och undersökningarna som utförts i denna uppsats visar att det faktiskt finns ett sådant nätverk.
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潘成達 and Shing-Tat Poon. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977443.
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Poon, Shing-Tat. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13787421.
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Haque, Mahbuba. "Comparison of Distance-Based Classifiers for Elliptically Contoured Distributions." Thesis, Uppsala universitet, Statistiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-328026.
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A simulation study is carried out to compare three distance-based classifiers for their misclassification and asymptotic distributions when the data follow certain elliptically contoured distributions. The data are generated from multivariate normal, multivariate t and multivariate normal mixture distributions with varying covariance structures, sample sizes and dimension sizes. In many of the simulated cases, the dimensions of the data are much larger than the sample size. The simulations show that for small dimension sizes, the centroid classifier generally performs better. The nearest neighbour classifier shows superior performance compared to the other classifiers when the covariance structure is of compound symmetry form. All three classifiers showed to have asymptotic normal distribution, regardless of the underlying distribution of the data.
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Zhang, Zuoshun. "Proper posterior distributions for some hierarchical models and roundoff effects in the Gibbs sampler /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
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Mai, Tobias [Verfasser], and Roland [Akademischer Betreuer] Speicher. "On the analytic theory of non-commutative distributions in free probability / Tobias Mai ; Betreuer: Roland Speicher." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2017. http://d-nb.info/1129174263/34.
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Dominicy, Yves. "Quantile-based inference and estimation of heavy-tailed distributions." Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209311.
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This thesis is divided in four chapters. The two first chapters introduce a parametric quantile-based estimation method of univariate heavy-tailed distributions and elliptical distributions, respectively. If one is interested in estimating the tail index without imposing a parametric form for the entire distribution function, but only on the tail behaviour, we propose a multivariate Hill estimator for elliptical distributions in chapter three. In the first three chapters we assume an independent and identically distributed setting, and so as a first step to a dependent setting, using quantiles, we prove in the last chapter the asymptotic normality of marginal sample quantiles for stationary processes under the S-mixing condition.<p><p><p>The first chapter introduces a quantile- and simulation-based estimation method, which we call the Method of Simulated Quantiles, or simply MSQ. Since it is based on quantiles, it is a moment-free approach. And since it is based on simulations, we do not need closed form expressions of any function that represents the probability law of the process. Thus, it is useful in case the probability density functions has no closed form or/and moments do not exist. It is based on a vector of functions of quantiles. The principle consists in matching functions of theoretical quantiles, which depend on the parameters of the assumed probability law, with those of empirical quantiles, which depend on the data. Since the theoretical functions of quantiles may not have a closed form expression, we rely on simulations.<p><p><p>The second chapter deals with the estimation of the parameters of elliptical distributions by means of a multivariate extension of MSQ. In this chapter we propose inference for vast dimensional elliptical distributions. Estimation is based on quantiles, which always exist regardless of the thickness of the tails, and testing is based on the geometry of the elliptical family. The multivariate extension of MSQ faces the difficulty of constructing a function of quantiles that is informative about the covariation parameters. We show that the interquartile range of a projection of pairwise random variables onto the 45 degree line is very informative about the covariation.<p><p><p>The third chapter consists in constructing a multivariate tail index estimator. In the univariate case, the most popular estimator for the tail exponent is the Hill estimator introduced by Bruce Hill in 1975. The aim of this chapter is to propose an estimator of the tail index in a multivariate context; more precisely, in the case of regularly varying elliptical distributions. Since, for univariate random variables, our estimator boils down to the Hill estimator, we name it after Bruce Hill. Our estimator is based on the distance between an elliptical probability contour and the exceedance observations. <p><p><p>Finally, the fourth chapter investigates the asymptotic behaviour of the marginal sample quantiles for p-dimensional stationary processes and we obtain the asymptotic normality of the empirical quantile vector. We assume that the processes are S-mixing, a recently introduced and widely applicable notion of dependence. A remarkable property of S-mixing is the fact that it doesn't require any higher order moment assumptions to be verified. Since we are interested in quantiles and processes that are probably heavy-tailed, this is of particular interest.<p><br>Doctorat en Sciences économiques et de gestion<br>info:eu-repo/semantics/nonPublished
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Wang, Juan. "Estimation of individual treatment effect via Gaussian mixture model." HKBU Institutional Repository, 2020. https://repository.hkbu.edu.hk/etd_oa/839.
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In this thesis, we investigate the estimation problem of treatment effect from Bayesian perspective through which one can first obtain the posterior distribution of unobserved potential outcome from observed data, and then obtain the posterior distribution of treatment effect. We mainly consider how to represent a joint distribution of two potential outcomes - one from treated group and another from control group, which can give us an indirect impression of correlation, since the estimation of treatment effect depends on correlation between two potential outcomes. The first part of this thesis illustrates the effectiveness of adapting Gaussian mixture models in solving the treatment effect problem. We apply the mixture models - Gaussian Mixture Regression (GMR) and Gaussian Mixture Linear Regression (GMLR)- as a potentially simple and powerful tool to investigate the joint distribution of two potential outcomes. For GMR, we consider a joint distribution of the covariate and two potential outcomes. For GMLR, we consider a joint distribution of two potential outcomes, which linearly depend on covariate. Through developing an EM algorithm for GMLR, we find that GMR and GMLR are effective in estimating means and variances, but they are not effective in capturing correlation between two potential outcomes. In the second part of this thesis, GMLR is modified to capture unobserved covariance structure (correlation between outcomes) that can be explained by latent variables introduced through making an important model assumption. We propose a much more efficient Pre-Post EM Algorithm to implement our proposed GMLR model with unobserved covariance structure in practice. Simulation studies show that Pre-Post EM Algorithm performs well not only in estimating means and variances, but also in estimating covariance.
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欒世武 and Shiwu Luan. "Structural inference of linear models for some families of error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31237502.
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Luan, Shiwu. "Structural inference of linear models for some families of error distributions /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19979368.
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Baek, Yeongcheon. "An interior point approach to constrained nonparametric mixture models /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5753.
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Ramsey, Joseph Daniel. "Expertise and mixture in automatic causal discovery /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2001. http://wwwlib.umi.com/cr/ucsd/fullcit?p3022219.
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Kravchuk, Olena. "Trigonometric scores rank procedures with applications to long-tailed distributions /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19314.pdf.
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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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Witkiewitz, Katie. "Predicting alcohol relapse using nonlinear dynamics and growth mixture modeling /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/9047.
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Jayaram, Vikram. "Reduced dimensionality hyperspectral classification using finite mixture models." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Wirgen, Isak, and Douglas Rube. "Supervised fraud detection of mobile money transactions on different distributions of imbalanced data : A comparative study of the classification methods logistic regression, random forest, and support vector machine." Thesis, Uppsala universitet, Statistiska institutionen, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-446108.
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The purpose of this paper is to compare the classification methods logistic regression, random forest, and support vector machine´s performance of detecting mobile money transaction fraud. Their performance will be evaluated on different distributions of imbalanced data in a supervised framework. Model performance will be evaluated from a variety of metrics to capture the full model performance. The results show that random forest attained the highest overall performance, followed by logistic regression. Support vector machine attained the worst overall performance and produced no useful classification of fraudulent transactions. In conclusion, the study suggests that better results could be achieved with actions such as improvements of the classification algorithms as well as better feature selection, among others.
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Ford, Elizabeth. "Barabási-Albert random graphs, scale-free distributions and bounds for approximation through Stein's method." Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:b1091661-33b5-47fe-912c-61286159904a.
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Barabási-Albert random graph models are a class of evolving random graphs that are frequently used to model social networks with scale-free degree distributions. It has been shown that Barabási-Albert random graph models have asymptotic scale-free degree distributions as the size of the graph tends to infinity. Real world networks, however, have finite size so it is important to know how close the degree distribution of a Barabási-Albert random graph of a given size is to its asymptotic distribution. Stein’s method is chosen as one main method for obtaining explicit bounds for the distance between distributions. We derive a new version of Stein’s method for a class of scale-free distributions and apply the method to a Barabási-Albert random graph. We compare the evolution of a sequence of Barabási-Albert random graphs with continuous time stochastic processes motivated by Yule’s model for evolution. Through a coupling of the models we bound the total variation distance between their degree distributions. Using these bounds, we extend degree distribution bounds that we find for specific models within the scheme to find bounds for every member of the scheme. We apply the Azuma-Hoeffding inequality and Chernoff bounds to find bounds between the degree sequences of the random graph models and the given scale-free distribution. These bounds prove that the degree sequences converge completely (and therefore also converge almost surely) to our scale-free distribution. We discuss the relationship between the random graph processes and the Chinese restaurant process. Aided by the construction of an inhomogeneous Markov chain, we apply our results for the degree distribution in a Barabási-Albert random graph to a particular statistic of the Chinese restaurant process. Finally, we explore how our methods can be adapted and extended to other evolving random graph processes. We study a Bernoulli evolving random graph process, for which we bound the distance between its degree distribution and a geometric distribution and we bound the distance between the number of triangles in the graph and a normal distribution.
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Chang, Soong Uk. "Clustering with mixed variables /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19086.pdf.
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Liang, Yi. "Likelihood ratio test for the presence of cured individuals : a simulation study /." Internet access available to MUN users only, 2002. http://collections.mun.ca/u?/theses,157472.
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Dean, Nema. "Variable selection and other extensions of the mixture model clustering framework /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/8943.
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Wang, Yunli. "Mass Spectrum Analysis of a Substance Sample Placed into Liquid Solution." Thesis, North Dakota State University, 2011. https://hdl.handle.net/10365/28881.
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Mass spectrometry is an analytical technique commonly used for determining elemental composition in a substance sample. For this purpose, the sample is placed into some liquid solution called liquid matrix. Unfortunately, the spectrum of the sample is not observable separate from that of the solution. Thus, it is desired to distinguish the sample spectrum. The analysis is usually based on the comparison of the mixed spectrum with the one of the sole solution. Introducing the missing information about the origin of observed spectrum peaks, the author obtains a classic set up for the Expectation-Maximization (EM) algorithm. The author proposed a mixture modeling the spectrum of the liquid solution as well as that of the sample. A bell-shaped probability mass function obtained by discretization of the univariate Gaussian probability density function was proposed or serving as a mixture component. The E- and M- steps were derived under the proposed model. The corresponding R program is written and tested on a small but challenging simulation example. Varying the number of mixture components for the liquid matrix and sample, the author found the correct model according to Bayesian Information Criterion. The initialization of the EM algorithm is a difficult standalone problem that was successfully resolved for this case. The author presents the findings and provides results from the simulation example as well as corresponding illustrations supporting the conclusions.
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Bletery, Quentin. "Analyse probabiliste et multi-données de la source de grands séismes." Thesis, Nice, 2015. http://www.theses.fr/2015NICE4092/document.
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Les séismes sont le résultat de glissements rapides le long de failles actives chargées en contraintes par le mouvement des plaques tectoniques. Il est aujourd'hui établi, au moins pour les grands séismes, que la distribution de ce glissement rapide le long des failles pendant les séismes est hétérogène. Imager la complexité de ces distributions de glissement constitue un enjeu majeur de la sismologie en raison des implications potentielles dans la compréhension de la genèse des séismes et la possibilité associée de mieux anticiper le risque sismique et les tsunamis. Pour améliorer l'imagerie de ces distributions de glissement co-sismique, trois axes peuvent être suivis: augmenter les contraintes sur les modèles en incluant plus d'observations dans les inversions, améliorer la modélisation physique du problème direct et progresser dans le formalisme de résolution du problème inverse. Dans ce travail de thèse, nous explorons ces trois axes à travers l'étude de deux séismes majeurs: les séisme de Tohoku-Oki (Mw 9.0) et de Sumatra-Andaman (Mw 9.1-9.3) survenus en 2011 et 2004, respectivement<br>Earthquakes are the results of rapid slip on active faults loaded in stress by the tectonic plates motion. It is now establish - at least for large earthquakes - that the distribution of this rapid slip along the rupturing faults is heterogeneous. Imaging the complexity of such slip distributions is one the main challenges in seismology because of the potential implications on understanding earthquake genesis and the associated possibility to better anticipate devastating shaking and tsunami. To improve the imaging of such co-seismic slip distributions, three axes may be followed: increase the constraints on the source models by including more observations into the inversions, improve the physical modeling of the forward problem and improve the formalism to solve the inverse problem. In this PhD thesis, we explore these three axes by studying two recent major earthquakes: the Tohoku-Oki (Mw 9.0) and Sumatra-Andaman (Mw 9.1-9.3) earthquakes, which occured in 2011 and 2004 respectively
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Ewertzh, Jacob. "Bankruptcy Distributions and Modelling for Swedish Companies Using Logistic Regression." Thesis, KTH, Matematisk statistik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-252329.
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This thesis discusses the concept of bankruptcy, or default, for Swedish companies. The actual distribution over time is considered both on aggregate level and within different industries. Several models are constructed to best possible describe the default frequency. Mainly logistic regression models are designed for this purpose, but various other models are considered. Some of these are constructed for comparison and for the ambition to produce the most accurate model possible. A large data set of nearly 30 million quarterly observations is used in the analysis. Taking into account micro and macro economic data. The derived models cover different time periods, considering different variables and display varying levels of accuracy. The most exact model is a logistic regression model considering both micro and macro data. It is tested both in sample and out of sample and perform very well in both areas. This model is estimated on first a subset of the data set to be able to compare with a real scenario. Then an equivalent model is constructed from the whole data set to best possibly describe future scenarios. Here Vector Auto-Regressive (VAR) models, and empirical models constructed by OLS regression estimating the firm values, are used in combination with the logistic regression model to predict the future. All three models are used to describe the most likely scenarios, as well as the worst case scenarios. From the worst case scenarios risk measures, such as the empirical value at risk, can be derived. From all this analysis the most significant results are compiled. Namely, that the Logistic regression model performs remarkably well both in-sample and out-of-sample, if macro variables are taken into account. Further, the future results are harder to interpret. Yet, the analysis has arguments for prediction accuracy and interesting results of a continued low default frequency within the next year.<br>Den här uppsatsen avhandlar konceptet konkurs, för svenska företag. Den faktiska konkursfördelningen över tid analyseras, både på en sammanlagd nivå och inom olika industrier. Flera modeller konstrueras i syfte att bäst beskriva konkursfördelningen. Huvudsakligen är logistiska regressions modeller utformade för detta syfte, men andra typer av modeller är inkluderade i analysen. Några av dessa modeller är skapade för jämförelse, men också för att kunna producera en så exakt modell som möjligt. Ett stort data set med nästan 30 miljoner kvartalsvisa observationer används i analysen. Mikro- och makroekonomiska faktorer är inkluderade i detta data set. De framtagna modellerna omfattar olika tidsperioder mellan 1990–2018, tar in olika faktorer i analysen och visar på olika nivåer av noggrannhet. Modellen som har högst förklaringsgrad är en logistisk regressionsmodell som tar hänsyn till både mikro- och makroekonomiska faktorer. Denna modell analyseras både i och utanför sitt samplingsintervall, och visar på goda resultat i båda områdena. Modellen är först skattad på en delmängd av tidsperioden, för att kunna jämföra den förutspådda fördelningen med en faktisk fördelning. Sedan är en ekvivalent modell skattad på hela intervallet, för att bäst möjligt förutspå framtida scenarion. För detta syfte är Logistiska regressionsmodellen kombinerad med Vektor Autoregressiva (VAR)-modeller som förutspår makroekonomiska faktorer, och empiriska regressionsmodeller som förutspår mikroekonomiska faktorer. Alla tre modelltyper används för att kunna beskriva det mest sannolika scenariot, samt de värsta tänkbara scenariona. Från de värsta tänkbara scenariona kan riskmått, så som empiriska Value at Risk, tas fram. All analys producerar resultat och de viktigaste sammanställs. Dessa är att den logistiska regression modell som tar hänsyn till makroekonomiska faktorer ger bra resultat både i och utanför samplingsintervallet. Vidare är de framtida simulerade resultaten svårare att tolka, men den genomförda analysen har argument för exakthet i förutsägelserna. Därmed presenteras ett troligt framtida scenario med fortsatt låg konkurs frekvens inom det närmaste året.
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Hasan, Abeer. "A Study of non-central Skew t Distributions and their Applications in Data Analysis and Change Point Detection." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1371055538.
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Ley, Christophe. "Univariate and multivariate symmetry: statistical inference and distributional aspects." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210029.
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This thesis deals with several statistical and probabilistic aspects of symmetry and asymmetry, both in a univariate and multivariate context, and is divided into three distinct parts.<p><p>The first part, composed of Chapters 1, 2 and 3 of the thesis, solves two conjectures associated with multivariate skew-symmetric distributions. Since the introduction in 1985 by Adelchi Azzalini of the most famous representative of that class of distributions, namely the skew-normal distribution, it is well-known that, in the vicinity of symmetry, the Fisher information matrix is singular and the profile log-likelihood function for skewness admits a stationary point whatever the sample under consideration. Since that moment, researchers have tried to determine the subclasses of skew-symmetric distributions who suffer from each of those problems, which has led to the aforementioned two conjectures. This thesis completely solves these two problems.<p><p>The second part of the thesis, namely Chapters 4 and 5, aims at applying and constructing extremely general skewing mechanisms. As such, in Chapter 4, we make use of the univariate mechanism of Ferreira and Steel (2006) to build optimal (in the Le Cam sense) tests for univariate symmetry which are very flexible. Actually, their mechanism allowing to turn a given symmetric distribution into any asymmetric distribution, the alternatives to the null hypothesis of symmetry can take any possible shape. These univariate mechanisms, besides that surjectivity property, enjoy numerous good properties, but cannot be extended to higher dimensions in a satisfactory way. For this reason, we propose in Chapter 5 different general mechanisms, sharing all the nice properties of their competitors in Ferreira and Steel (2006), but which moreover can be extended to any dimension. We formally prove that the surjectivity property holds in dimensions k>1 and we study the principal characteristics of these new multivariate mechanisms.<p><p>Finally, the third part of this thesis, composed of Chapter 6, proposes a test for multivariate central symmetry by having recourse to the concepts of statistical depth and runs. This test extends the celebrated univariate runs test of McWilliams (1990) to higher dimensions. We analyze its asymptotic behavior (especially in dimension k=2) under the null hypothesis and its invariance and robustness properties. We conclude by an overview of possible modifications of these new tests./<p><p>Cette thèse traite de différents aspects statistiques et probabilistes de symétrie et asymétrie univariées et multivariées, et est subdivisée en trois parties distinctes.<p><p>La première partie, qui comprend les chapitres 1, 2 et 3 de la thèse, est destinée à la résolution de deux conjectures associées aux lois skew-symétriques multivariées. Depuis l'introduction en 1985 par Adelchi Azzalini du plus célèbre représentant de cette classe de lois, à savoir la loi skew-normale, il est bien connu qu'en un voisinage de la situation symétrique la matrice d'information de Fisher est singulière et la fonction de vraisemblance profile pour le paramètre d'asymétrie admet un point stationnaire quel que soit l'échantillon considéré. Dès lors, des chercheurs ont essayé de déterminer les sous-classes de lois skew-symétriques qui souffrent de chacune de ces problématiques, ce qui a mené aux deux conjectures précitées. Cette thèse résoud complètement ces deux problèmes.<p><p>La deuxième partie, constituée des chapitres 4 et 5, poursuit le but d'appliquer et de proposer des méchanismes d'asymétrisation très généraux. Ainsi, au chapitre 4, nous utilisons le méchanisme univarié de Ferreira and Steel (2006) pour construire des tests de symétrie univariée optimaux (au sens de Le Cam) qui sont très flexibles. En effet, leur méchanisme permettant de transformer une loi symétrique donnée en n'importe quelle loi asymétrique, les contre-hypothèses à la symétrie peuvent prendre toute forme imaginable. Ces méchanismes univariés, outre cette propriété de surjectivité, possèdent de nombreux autres attraits, mais ne permettent pas une extension satisfaisante aux dimensions supérieures. Pour cette raison, nous proposons au chapitre 5 des méchanismes généraux alternatifs, qui partagent toutes les propriétés de leurs compétiteurs de Ferreira and Steel (2006), mais qui en plus sont généralisables à n'importe quelle dimension. Nous démontrons formellement que la surjectivité tient en dimension k > 1 et étudions les caractéristiques principales de ces nouveaux méchanismes multivariés.<p><p>Finalement, la troisième partie de cette thèse, composée du chapitre 6, propose un test de symétrie centrale multivariée en ayant recours aux concepts de profondeur statistique et de runs. Ce test étend le célèbre test de runs univarié de McWilliams (1990) aux dimensions supérieures. Nous en analysons le comportement asymptotique (surtout en dimension k = 2) sous l'hypothèse nulle et les propriétés d'invariance et de robustesse. Nous concluons par un aperçu sur des modifications possibles de ces nouveaux tests.<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished
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Bright, Leslie William. "Matrix-analytic methods in applied probability /." Title page, table of contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phb855.pdf.
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Elamir, Elsayed Ali Habib. "Probability distribution theory, generalisations and applications of L-moments." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3987/.
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In this thesis, we have studied L-moments and trimmed L-moments (TL-moments) which are both linear functions of order statistics. We have derived expressions for exact variances and covariances of sample L-moments and of sample TL-moments for any sample size n in terms of first and second-order moments of order statistics from small conceptual sample sizes, which do not depend on the actual sample size n. Moreover, we have established a theorem which characterises the normal distribution in terms of these second-order moments and the characterisation suggests a new test of normality. We have also derived a method of estimation based on TL-moments which gives zero weight to extreme observations. TL-moments have certain advantages over L-moments and method of moments. They exist whether or not the mean exists (for example the Cauchy distribution) and they are more robust to the presence of outliers. Also, we have investigated four methods for estimating the parameters of a symmetric lambda distribution: maximum likelihood method in the case of one parameter and L-moments, LQ-moments and TL-moments in the case of three parameters. The L-moments and TL-moments estimators are in closed form and simple to use, while numerical methods are required for the other two methods, maximum likelihood and LQ-moments. Because of the flexibility and the simplicity of the lambda distribution, it is useful in fitting data when, as is often the case, the underlying distribution is unknown. Also, we have studied the symmetric plotting position for quantile plot assuming a symmetric lambda distribution and conclude that the choice of the plotting position parameter depends upon the shape of the distribution. Finally, we propose exponentially weighted moving average (EWMA) control charts to monitor the process mean and dispersion using the sample L-mean and sample L-scale and charts based on trimmed versions of the same statistics. The proposed control charts limits are less influenced by extreme observations than classical EWMA control charts, and lead to tighter limits in the presence of out-of-control observations.
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Hazarika, Subhashis. "Statistical and Machine Learning Approaches For Visualizing and Analyzing Large-Scale Simulation Data." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1574692702479196.
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Jónsson, Ragner H. "Adaptive subband coding of video using probability distribution models." Diss., Georgia Institute of Technology, 1994. http://hdl.handle.net/1853/14453.
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