Relevant bibliographies by topics / Student-t Distribution

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Academic literature on the topic 'Student-t Distribution'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Student-t Distribution"

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Moreno-Arenas, Germán, Guillermo Martínez-Flórez, and Heleno Bolfarine. "Power Birnbaum-Saunders Student t distribution." Revista Integración 35, no. 1 (2017): 51–70. http://dx.doi.org/10.18273/revint.v35n1-2017004.

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Chen, William W. S. "On Finding Geodesic Equation of Student T Distribution." Journal of Mathematics Research 9, no. 2 (2017): 32. http://dx.doi.org/10.5539/jmr.v9n2p32.

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Student t distribution has been widely applied in the course of statistics. In this paper, we focus on finding a geodesic equation of the two parameter student t distributions. To find this equation, we applied both the well-known Darboux Theorem and a triply of partial differential equations taken from Struik D.J. (Struik, D.J., 1961) or Grey A (Grey A., 1993), As expected, the two different approaches reach the same type of results. The solution proposed in this paper could be used as a general solution of the geodesic equation for the student t distribution.
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Nugroho, Didit Budi, Agus Priyono, and Bambang Susanto. "SKEW NORMAL AND SKEW STUDENT-T DISTRIBUTIONS ON GARCH(1,1) MODEL." MEDIA STATISTIKA 14, no. 1 (2021): 21–32. http://dx.doi.org/10.14710/medstat.14.1.21-32.

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The Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) type models have become important tools in financial application since their ability to estimate the volatility of financial time series data. In the empirical financial literature, the presence of skewness and heavy-tails have impacts on how well the GARCH-type models able to capture the financial market volatility sufficiently. This study estimates the volatility of financial asset returns based on the GARCH(1,1) model assuming Skew Normal and Skew Student-t distributions for the returns errors. The models are applied to daily returns of FTSE100 and IBEX35 stock indices from January 2000 to December 2017. The model parameters are estimated by using the Generalized Reduced Gradient Non-Linear method in Excel’s Solver and also the Adaptive Random Walk Metropolis method implemented in Matlab. The estimation results from fitting the models to real data demonstrate that Excel’s Solver is a promising way for estimating the parameters of the GARCH(1,1) models with non-Normal distribution, indicated by the accuracy of the estimation of Excel’s Solver. The fitting performance of models is evaluated by using log-likelihood ratio test and it indicates that the GARCH(1,1) model with Skew Student-t distribution provides the best fitting, followed by Student-t, Skew-Normal, and Normal distributions.
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Chen, Zexun, Bo Wang, and Alexander N. Gorban. "Multivariate Gaussian and Student-t process regression for multi-output prediction." Neural Computing and Applications 32, no. 8 (2019): 3005–28. http://dx.doi.org/10.1007/s00521-019-04687-8.

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AbstractGaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to reformulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, reformulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student-t distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student-t process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real-data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.
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Ceretta, Paulo Sérgio, Fernanda Galvão De Barba, Kelmara Mendes Vieira, and Fernando Casarin. "Previsão da volatilidade intradiária: análise das distribuições alternativas." Brazilian Review of Finance 9, no. 2 (2011): 209. http://dx.doi.org/10.12660/rbfin.v9n2.2011.2586.

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Volatility forecasting has been of great interest both in academic and professional fields all over the world. However, there is no agreement about the best model to estimate
 volatility. New models include measures of skewness, changes of regimes and different distributions; few studies, though, have considered different distributions. This paper aims to
 investigate how the specification of a distribution influences the performance of volatility forecasting on Ibovespa intraday data, using the APARCH model. The forecasts were carried
 out assuming six distinct distributions: normal, skewed normal, t-student, skewed t-student, generalized and skewed generalized. The results evidence that the model considering the skewed t-student distribution offered the best fit to the data inside the sample, on the other hand, the model assuming a normal distribution provided a better out-of-the-sample performance forecast.
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Safiul Haq, M., and Shahjahan Khan. "Prediction distribution for a linear regression model with multivariate student-t error distribution." Communications in Statistics - Theory and Methods 19, no. 12 (1990): 4705–12. http://dx.doi.org/10.1080/03610929008830469.

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da Silva Braga, Altemir, Gauss M. Cordeiro, Edwin M. M. Ortega, and Giovana O. Silva. "The Odd Log-Logistic Student t Distribution: Theory and Applications." Journal of Agricultural, Biological and Environmental Statistics 22, no. 4 (2017): 615–39. http://dx.doi.org/10.1007/s13253-017-0301-x.

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Sales, Francisco Das Chagas Vieira, José Antonio Aleixo da Silva, Rinaldo Luiz Caraciolo Ferreira, and Fernando Henrique de Lima Gadelha. "AJUSTES DE MODELOS VOLUMÉTRICOS PARA O CLONE Eucalyptus grandis x E. urophylla CULTIVADOS NO AGRESTE DE PERNAMBUCO." FLORESTA 45, no. 4 (2015): 663. http://dx.doi.org/10.5380/rf.v45i4.37594.

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O presente trabalho teve como objetivo avaliar o ajuste de modelos volumétricos para um clone de Eucalyptus usando distribuição normal e t-Student, utilizando dados de um experimento implantado no Instituto Agronômico de Pernambuco (IPA) em São Bento do Una, PE. Para o ajuste dos modelos volumétricos de Silva e Bailey modificado, Chapman e Richard modificado, Schumacher e Hall e, Brody modificado, foram utilizados dados de 62 árvores cubadas rigorosamente pelo método de Smalian. Os critérios usados nas comparações das equações foi o valor ponderado (VP) entre o Índice de Ajuste corrigido (IAc) e o erro percentual absoluto médio (EPAM). De acordo com os resultados o modelo que mostrou melhores ajustes nas duas distribuições foi o de Schumacher e Hall, com melhores ajuste quando da distribuição t-Student. A distribuição t-Student promoveu melhorias nos ajustes das equações em relação à distribuição Normal, quando comparando as duas distribuições em cada equação.AbstractAdjustment of volumetric models for clone of Eucalyptus grandis x E. Urophylla grown on agreste, Pernambuco. This research aimed to evaluate the volumetric models fitting for Eucalyptus clone using normal and t-Student distributions, based on data from an experiment implanted at the Agronomic Institute of Pernambuco (IPA) in São Bento do Una, PE. In order to set the modified volumetric models of Silva and Bailey, modified Chapman and Richard, Schumacher and Hall, and modified Brody, we used data from 62 trees rigorously scaled by Smalian method. The criteria for equation comparing were the weighted value (PV) between the corrected index adjustment (IAc) and absolute mean error percentage (EPAM). According to the results, the model that best fits for the two distributions is Schumacher and Hall, with better adjustment related to the Student-t distribution. The t-Student distribution promoted improvements of equations regarding the Normal distribution, compared to the two distributions per equation.Keywords: Forest management; symmetric distributions; volume equations.
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Singh, Surbhi, Harsh Vikram Singh, and Anand Mohan. "Secure and Robust Watermarking Using Wavelet Transform and Student t-distribution." Procedia Computer Science 70 (2015): 442–47. http://dx.doi.org/10.1016/j.procs.2015.10.071.

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Wang, Zongyuan, and Weidong Zhou. "Robust Linear Filter with Parameter Estimation Under Student-t Measurement Distribution." Circuits, Systems, and Signal Processing 38, no. 6 (2018): 2445–70. http://dx.doi.org/10.1007/s00034-018-0972-8.

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Dissertations / Theses on the topic "Student-t Distribution"

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Mazviona, Batsirai Winmore. "Volatility forecasting using Double-Markov switching GARCH models under skewed Student-t distribution." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/12344.

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Includes bibliographical references.<br>This thesis focuses on forecasting the volatility of daily returns using a double Markov switching GARCH model with a skewed Student-t error distribution. The model was applied to individual shares obtained from the Johannesburg Stock Exchange (JSE). The Bayesian approach which uses Markov Chain Monte Carlo was used to estimate the unknown parameters in the model. The double Markov switching GARCH model was compared to a GARCH(1,1) model. Value at risk thresholds and violations ratios were computed leading to the ranking of the GARCH and double Markov switching GARCH models. The results showed that double Markov switching GARCH model performs similarly to the GARCH model based on the ranking technique employed in this thesis.
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Busato, Erick Andrade. "Função de acoplamento t-Student assimetrica : modelagem de dependencia assimetrica." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305857.

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Orientador: Luiz Koodi Hotta<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T14:00:24Z (GMT). No. of bitstreams: 1 Busato_ErickAndrade_M.pdf: 4413458 bytes, checksum: b9c4c39b4639c19e685bae736fc86c4f (MD5) Previous issue date: 2008<br>Resumo: A família de distribuições t-Student Assimétrica, construída a partir da mistura em média e variância da distribuição normal multivariada com a distribuição Inversa Gama possui propriedades desejáveis de flexibilidade para as mais diversas formas de assimetria. Essas propriedades são exploradas na construção de funções de acoplamento que possuem dependência assimétrica. Neste trabalho são estudadas as características e propriedades da distribuição t-Student Assimétrica e a construção da respectiva função de acoplamento, fazendo-se uma apresentação de diferentes estruturas de dependência que pode originar, incluindo assimetrias da dependência nas caudas. São apresentados métodos de estimação de parâmetros das funções de acoplamento, com aplicações até a terceira dimensão da cópula. Essa função de acoplamento é utilizada para compor um modelo ARMA-GARCHCópula com marginais de distribuição t-Student Assimétrica, que será ajustado para os logretornos de preços do Petróleo e da Gasolina, e log-retornos do Índice de Óleo AMEX, buscando o melhor ajuste, principalmente, para a dependência nas caudas das distribuições de preços. Esse modelo será comparado, através de medidas de Valor em Risco e AIC, além de outras medidas de bondade de ajuste, com o modelo de Função de Acoplamento t-Student Simétrico.<br>Abstract: The Skewed t-Student distribution family, constructed upon the multivariate normal mixture distribution, known as mean-variance mixture, composed with the Inverse-Gamma distribution, has many desirable flexibility properties for many distribution asymmetry structures. These properties are explored by constructing copula functions with asymmetric dependence. In this work the properties and characteristics of the Skewed t-Student distribution and the construction of a respective copula function are studied, presenting different dependence structures that the copula function generates, including tail dependence asymmetry. Parameter estimation methods are presented for the copula, with applications up to the 3rd dimension. This copula function is used to compose an ARMAGARCH- Copula model with Skewed t-Student marginal distribution that is adjusted to logreturns of Petroleum and Gasoline prices and log-returns of the AMEX Oil Index, emphasizing the return's tail distribution. The model will be compared, by the means of the VaR (Value at Risk) and Akaike's Information Criterion, along with other Goodness-of-fit measures, with models based on the Symmetric t-Student Copula.<br>Mestrado<br>Mestre em Estatística
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Ali, Mohamed Khadar. "Applying Value at Risk (VaR) analysis to Brent Blend Oil prices." Thesis, Högskolan i Gävle, Avdelningen för ekonomi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-10798.

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The purpose with this study is to compare four different models to VaR in terms of accuracy, namely Historical Simulation (HS), Simple Moving Average (SMA), Exponentially Weighted Moving Average (EWMA) and Exponentially Weighted Historical Simulation (EWHS). These VaR models will be applied to one underlying asset which is the Brent Blend Oil using these confidence levels 95 %, 99 % and 99, 9 %. Concerning the return of the asset the models under two different assumptions namely student t-distribution and normal distribution will be studied
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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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Ozturk, Kevser. "Exchange Rate Volatility: The Case Of Turkey." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12608026/index.pdf.

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In this study, different from previous studies, the explanatory power of Student-t distribution is compared to normal distribution by employing both standard GARCH and EGARCH models to dollar/ lira (USD/TRY) exchange rate. Then the impact of Central Bank of Republic of the Turkey&rsquo<br>s (CBRT) decisions and actions on both the level of exchange rate and the volatility is investigated. Moreover the relationship between volatility and market liquidity is examined using spot foreign exchange (FX) market volume as a proxy. The results reveal that, in contrast to preceding findings, Student-t could not capture the leptokurtic property better than normal distribution does. Furthermore, an increase in Turkish government benchmark bond rates, CBRT FX purchase interventions and announcement of suspending/ decreasing-the-amount-of FX auctions lead Turkish lira to depreciate. Because of the significant positive leverage effect, the results of GARCH and EGARCH variance equations differ so much. Thereby the results should be evaluated cautiously. In addition it is observed that, only EGARCH model gives significant results when the spot market trading volume is included in the models
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Ofe, Hosea, and Peter Okah. "Value at Risk: A Standard Tool in Measuring Risk : A Quantitative Study on Stock Portfolio." Thesis, Umeå universitet, Handelshögskolan vid Umeå universitet, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-45303.

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The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.
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Ashurbekova, Karina. "High-dimensional robust structure learning." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAT100.

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L'apprentisage de structure de graphes est un problème essentiel dans de nombreuses applications, i.e. génétiques, neuroscience.L'estimation de la matrice de covariance/précision est le point crucial. Les techniques usuelles souffrent de deux problèmes. Le premier problème est la robustesse aux données non gaussiennes. Le second problème est le manque de données quand le nombre de paramètres à estimer est trop grand devant la taille de l'échantillon disponible. L'objectif de cette thèse est de fournir des méthodes robustes et adaptée à une faible taille d'échantillon.La première contribution de cette thèse considère les estimateurs de maximum de vraisemblance de la matrice de covariance avec shrinkage sous l'hypothèse de distributions à queue lourde et moyenne inconnue. La difficulté principale est le choix du paramètre de régularisation. Nous dérivons une expression explicite du coefficient de shrinkage pour toute distribution elliptique. Nous proposons aussi un algorithm dans le cas de distribution de Student multivariée qui est appliqué à des données simulées et des données réelles.La deuxième contribution concerne l'estimation de matrice de précision parcimonieuse pour des données non gaussiennes. En partant des résultats de la littérature, nous avons généralisé ceux-ci à des modèles de mélanges en grande dimension pour une sous-classe de famille de distribution elliptique.Pour finir, nous avons testé nos approches sur des données réelles d'IRMf. La structure estimée est soit la correlation soit la correlation partielle. Nous proposons une nouvelle construction de graphes prenant en compte la correlation et la correlation partielle. Cette nouvelle approche est validée sur des simulations et des données réelles<br>Structure learning in graphical models is an essential topic in different application areas, i.e., genetics, neuroscience. The crucial part of this model is the estimation of covariance/precision matrices. Traditional techniques for handling this problem suffer from two main issues. The first one is the lack of robustness when samples are assumed to follow a Gaussian distribution. The second one is the lack of data when the number of parameters to estimate is too large compared to the number of samples. Thus this thesis aims to build robust high-dimensional models for covariance and precision matrices estimation.The first question we address in the manuscript is the link between zero elements of precision matrices and the measure of the relationship between variables it reveals for different distributions.par In the first main contribution of this thesis we consider the shrinked likelihood-based estimators of the covariance matrix under the assumption of heavy-tailed distribution with unknown mean vector. The main difficulty at this point is the choice of the regularization parameters. We provide a closed-form expression of an optimal shrinkage coefficient for any sample distribution in the elliptical family. Based on these results, an algorithm for the case of the multivariate t-distribution with the simulated and real data is presented.The second contribution is dealing with sparse precision matrix estimation for the non-Gaussian data. Starting with the traditional techniques, we are able to generalize results for the high-dimensional mixture models for the subclass of elliptical family.Finally, we test our graph structure learning approach on brain signals using fMRI. The structure induced by both the correlation and the partial correlation is considered. We then propose a new graph construction method taking into account both conditional and marginal independences. The proposed approach shows better results than classical algorithms
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Kim, Young Il. "Essays on Volatility Risk, Asset Returns and Consumption-Based Asset Pricing." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211912340.

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Freire, Paulo Guilherme de Lima. "Segmentação de placas de esclerose múltipla em imagens de ressonância magnética usando modelos de mistura de distribuições t-Student e detecção de outliers." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7736.

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Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-22T11:50:45Z No. of bitstreams: 1 DissPGLF.pdf: 2510277 bytes, checksum: ac0bc495fe911118e100ddeeaea3b4d9 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:47:09Z (GMT) No. of bitstreams: 1 DissPGLF.pdf: 2510277 bytes, checksum: ac0bc495fe911118e100ddeeaea3b4d9 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-10T14:47:16Z (GMT) No. of bitstreams: 1 DissPGLF.pdf: 2510277 bytes, checksum: ac0bc495fe911118e100ddeeaea3b4d9 (MD5)<br>Made available in DSpace on 2016-10-10T14:47:24Z (GMT). No. of bitstreams: 1 DissPGLF.pdf: 2510277 bytes, checksum: ac0bc495fe911118e100ddeeaea3b4d9 (MD5) Previous issue date: 2016-02-15<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Multiple Sclerosis (MS) is an inflammatory demyelinating (that is, with myelin loss) disease of the Central Nervous System (CNS). It is considered an autoimmune disease in which the immune system wrongly recognizes the myelin sheath of the CNS as an external element and attacks it, resulting in inflammation and scarring (sclerosis) of multiple areas of CNS’s white matter. Multi-contrast magnetic resonance imaging (MRI) has been successfully used in diagnosing and monitoring MS due to its excellent properties such as high resolution and good differentiation between soft tissues. Nowadays, the preferred method to segment MS lesions is the manual segmentation, which is done by specialists with limited help of a computer. However, this approach is tiresome, expensive and prone to error due to inter- and intra-variability between observers caused by low contrast on lesion edges. The challenge in automatic detection and segmentation of MS lesions in MR images is related to the variability of size and location of lesions, low contrast due to partial volume effect and the high range of forms that lesions can take depending on the stage of the disease. Recently, many researchers have turned their efforts into developing techniques that aim to accurately measure volumes of brain tissues and MS lesions, and also to reduce the amount of time spent on image analysis. In this context, this project proposes the study and development of an automatic computational technique based on an outlier detection approach, Student’s t-distribution finite mixture models and probabilistic atlases to segment and measure MS lesions volumes in MR images.<br>Esclerose Múltipla (EM) é uma doença inflamatória e desmielinizante (isto é, com perda de mielina) do sistema nervoso central (SNC). É considerada uma doença autoimune a qual o sistema imunológico reconhece erroneamente a bainha de mielina do SNC como um elemento externo e então a ataca, resultando em inflamação e formação de cicatrizes gliais (escleroses) em múltiplas áreas da substância branca do SNC. O imageamento multi- contraste por ressonância magnética (RM) tem sido usado clinicamente com muito sucesso para o diagnóstico e monitoramento da EM devido às suas excelentes propriedades como alta resolução e boa diferenciação de tecidos moles. Atualmente, o método utilizado para a segmentação de lesões de EM é o delineamento manual em imagens 3D de RM, o qual é realizado por especialistas com ajuda limitada do computador. Entretanto, tal procedimento é custoso e propenso à variabilidade inter e intraobservadores devido ao baixo contraste das bordas das lesões. A grande dificuldade na detecção e segmentação automáticas das le- sões de EM em imagens de RM está associada às suas variações no tamanho e localização, baixo contraste decorrente do efeito de volume parcial e o amplo espectro de aparências (realçadas, não-realçadas, black-holes) que elas podem ter, dependendo do estado evolutivo da doença. Atualmente, vários pesquisadores têm voltado seus esforços para o desenvol- vimento de técnicas que visam diminuir o tempo gasto na análise das imagens e medir, de maneira mais precisa, o volume dos tecidos cerebrais e das lesões de EM. Nesse contexto, este projeto propõe o estudo e o desenvolvimento de uma técnica computacional automá- tica, baseada na abordagem de detecção de outliers e usando modelos de misturas finitas de distribuições t-Student e atlas probabilísticos para a segmentação e medição do volume de lesões de EM em imagens de RM.<br>FAPESP: 2014/00019-6
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Blad, Wiktor, and Vilim Nedic. "GARCH models applied on Swedish Stock Exchange Indices." Thesis, Uppsala universitet, Statistiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-386185.

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In the financial industry, it has been increasingly popular to measure risk. One of the most common quantitative measures for assessing risk is Value-at-Risk (VaR). VaR helps to measure extreme risks that an investor is exposed to. In addition to acquiring information of the expected loss, VaR was introduced in the regulatory frameworks of Basel I and II as a standardized measure of market risk. Due to necessity of measuring VaR accurately, this thesis aims to be a contribution to the research field of applying GARCH-models to financial time series in order to forecast the conditional variance and find accurate VaR-estimations. The findings in this thesis is that GARCH-models which incorporate the asymmetric effect of positive and negative returns perform better than a standard GARCH. Further on, leptokurtic distributions have been found to outperform normal distribution. In addition to various models and distributions, various rolling windows have been used to examine how the forecasts differ given window lengths.
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Books on the topic "Student-t Distribution"

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Bilodeau, M. Stein estimation under elliptical distribution, power of F-tests under student-T distribution and tests of correlation in USR models. [s.n.], 1986.

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Ahsanullah, Mohammad, B. M. Golam Kibria, and Mohammad Shakil. Normal and Student´s t Distributions and Their Applications. Atlantis Press, 2014. http://dx.doi.org/10.2991/978-94-6239-061-4.

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Bilodeau, Martin R. Stein estimation under elliptical distribution, power of F-tests under student-T distribution and tests of correlation in Sur models. 1986.

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Dodgson, J. H. The effect of a preliminary test of normality using /b1 on Students' t-distribution. 1987.

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Ferreira, Eliel Alves, and João Vicente Zamperion. Excel: Uma ferramenta estatística. Brazil Publishing, 2021. http://dx.doi.org/10.31012/978-65-5861-400-5.

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This study aims to present the concepts and methods of statistical analysis using the Excel software, in a simple way aiming at a greater ease of understanding of students, both undergraduate and graduate, from different areas of knowledge. In Excel, mainly Data Analysis Tools will be used. For a better understanding, there are, in this book, many practical examples applying these tools and their interpretations, which are of paramount importance. In the first chapter, it deals with introductory concepts, such as introduction to Excel, the importance of statistics, concepts and definitions. Being that in this will be addressed the subjects of population and sample, types of data and their levels of measurement. Then it brings a detailed study of Descriptive Statistics, where it will be studied percentage, construction of graphs, frequency distribution, measures of central tendency and measures of dispersion. In the third chapter, notions of probability, binomial and normal probability distribution will be studied. In the last chapter, Inferential Statistics will be approached, starting with the confidence interval, going through the hypothesis tests (F, Z and t tests), ending with the statistical study of the correlation between variables and simple linear regression. It is worth mentioning that the statistical knowledge covered in this book can be useful for, in addition to students, professionals who want to improve their knowledge in statistics using Excel.
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Book chapters on the topic "Student-t Distribution"

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Ahsanullah, Mohammad, B. M. Golam Kibria, and Mohammad Shakil. "Student’s $$t$$ t Distribution." In Normal and Student´s t Distributions and Their Applications. Atlantis Press, 2014. http://dx.doi.org/10.2991/978-94-6239-061-4_3.

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Ahsanullah, Mohammad, B. M. Golam Kibria, and Mohammad Shakil. "Normal Distribution." In Normal and Student´s t Distributions and Their Applications. Atlantis Press, 2014. http://dx.doi.org/10.2991/978-94-6239-061-4_2.

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Ahsanullah, Mohammad, B. M. Golam Kibria, and Mohammad Shakil. "Characterizations of Student’s t Distribution." In Normal and Student´s t Distributions and Their Applications. Atlantis Press, 2014. http://dx.doi.org/10.2991/978-94-6239-061-4_9.

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Grigelionis, Bronius. "Student-Lévy Processes." In Student’s t-Distribution and Related Stochastic Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31146-8_4.

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Grigelionis, Bronius. "Student Diffusion Processes." In Student’s t-Distribution and Related Stochastic Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31146-8_6.

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Grigelionis, Bronius. "Student OU-Type Processes." In Student’s t-Distribution and Related Stochastic Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31146-8_5.

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Ahsanullah, Mohammad, B. M. Golam Kibria, and Mohammad Shakil. "Characterizations of Normal Distribution." In Normal and Student´s t Distributions and Their Applications. Atlantis Press, 2014. http://dx.doi.org/10.2991/978-94-6239-061-4_8.

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Grigelionis, Bronius. "Student’s t-Distribution." In International Encyclopedia of Statistical Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-04898-2_648.

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Gooch, Jan W. "Student’s T-Distribution." In Encyclopedic Dictionary of Polymers. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-6247-8_15394.

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Quicke, Donald L. J., Buntika A. Butcher, and Rachel A. Kruft Welton. "Standard distributions in R." In Practical R for biologists: an introduction. CABI, 2021. http://dx.doi.org/10.1079/9781789245349.0335.

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Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.
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Conference papers on the topic "Student-t Distribution"

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Mairgiotis, Antonis, Lisimachos P. Kondi, and Yongyi Yang. "Dct/dwt blind multiplicative watermarking through student-t distribution." In 2017 IEEE International Conference on Image Processing (ICIP). IEEE, 2017. http://dx.doi.org/10.1109/icip.2017.8296335.

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Tang, Qingtao, Tao Dai, Li Niu, Yisen Wang, Shu-Tao Xia, and Jianfei Cai. "Robust Survey Aggregation with Student-t Distribution and Sparse Representation." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/394.

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Most existing survey aggregation methods assume that the sample data follow Gaussian distribution. However, these methods are sensitive to outliers, due to the thin-tailed property of the Gaussian distribution. To address this issue, we propose a robust survey aggregation method based on Student-t distribution and sparse representation. Specifically, we assume that the samples follow Student-$t$ distribution, instead of the common Gaussian distribution. Due to the Student-t distribution, our method is robust to outliers, which can be explained from both Bayesian point of view and non-Bayesian point of view. In addition, inspired by James-Stain estimator (JS) and Compressive Averaging (CAvg), we propose to sparsely represent the global mean vector by an adaptive basis comprising both data-specific basis and combined generic bases. Theoretically, we prove that JS and CAvg are special cases of our method. Extensive experiments demonstrate that our proposed method achieves significant improvement over the state-of-the-art methods on both synthetic and real datasets.
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Zhou, Yifan, and Simon Maskell. "Robust and Efficient Image Alignment Method Using the Student-t Distribution." In 2020 IEEE 23rd International Conference on Information Fusion (FUSION). IEEE, 2020. http://dx.doi.org/10.23919/fusion45008.2020.9190357.

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Botev, Zdravko I., and Pierre L'Ecuyer. "Efficient probability estimation and simulation of the truncated multivariate student-t distribution." In 2015 Winter Simulation Conference (WSC). IEEE, 2015. http://dx.doi.org/10.1109/wsc.2015.7408180.

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Amor, Nesrine, Seif Kahlaoui, and Souad Chebbi. "Unscented particle filter using student-t distribution with non-Gaussian measurement noise." In 2018 International Conference on Advanced Systems and Electric Technologies (IC_ASET). IEEE, 2018. http://dx.doi.org/10.1109/aset.2018.8379830.

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Takahashi, Hiroshi, Tomoharu Iwata, Yuki Yamanaka, Masanori Yamada, and Satoshi Yagi. "Student-t Variational Autoencoder for Robust Density Estimation." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/374.

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We propose a robust multivariate density estimator based on the variational autoencoder (VAE). The VAE is a powerful deep generative model, and used for multivariate density estimation. With the original VAE, the distribution of observed continuous variables is assumed to be a Gaussian, where its mean and variance are modeled by deep neural networks taking latent variables as their inputs. This distribution is called the decoder. However, the training of VAE often becomes unstable. One reason is that the decoder of VAE is sensitive to the error between the data point and its estimated mean when its estimated variance is almost zero. We solve this instability problem by making the decoder robust to the error using a Bayesian approach to the variance estimation: we set a prior for the variance of the Gaussian decoder, and marginalize it out analytically, which leads to proposing the Student-t VAE. Numerical experiments with various datasets show that training of the Student-t VAE is robust, and the Student-t VAE achieves high density estimation performance.
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Gai, Jiading, Yong Li, and Robert L. Stevenson. "Robust Bayesian PCA with Student’s t-distribution: The variational inference approach." In 2008 15th IEEE International Conference on Image Processing. IEEE, 2008. http://dx.doi.org/10.1109/icip.2008.4712011.

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Gai, Jiading, Yong Li, and Robert L. Stevenson. "An EM algorithm for robust Bayesian PCA with student’s t-distribution." In 2008 15th IEEE International Conference on Image Processing. IEEE, 2008. http://dx.doi.org/10.1109/icip.2008.4712344.

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Nugroho, Didit Budi, and Bambang Susanto. "Volatility modeling for IDR exchange rate through APARCH model with student-t distribution." In THE 4TH INTERNATIONAL CONFERENCE ON RESEARCH, IMPLEMENTATION, AND EDUCATION OF MATHEMATICS AND SCIENCE (4TH ICRIEMS): Research and Education for Developing Scientific Attitude in Sciences And Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4995120.

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Qiu, Mengdie, Zan Yang, Wei Nai, Dan Li, Yidan Xing, and Kai Li. "T-Distributed Stochastic Neighbor Embedding Based on Cockroach Swarm Optimization with Student Distribution Parameters." In 2021 IEEE 12th International Conference on Software Engineering and Service Science (ICSESS). IEEE, 2021. http://dx.doi.org/10.1109/icsess52187.2021.9522161.

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Reports on the topic "Student-t Distribution"

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Gibbons, Robert D., Donald Hedeker, and R. D. Bock. Multivariate Generalizations of Student's t-Distribution. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada229128.

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