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Some contributions to the analysis of skew data on the line and circlePewsey, Arthur Richard January 2002 (has links)
No description available.
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Bayesian inference on mixture models and their applicationsChang, Ilsung 16 August 2006 (has links)
Mixture models are useful in describing a wide variety of random phenomena because
of their flexibility in modeling. They have continued to receive increasing attention
over the years from both a practical and theoretical point of view. In their applications,
estimating the number of mixture components is often the main research
objective or the first step toward it. Estimation of the number of mixture components
heavily depends on the underlying distribution. As an extension of normal
mixture models, we introduce a skew-normal mixture model and adapt the reversible
jump Markov chain Monte Carlo algorithm to estimate the number of components
with some applications to biological data.
The reversible jump algorithm is also applied to the Cox proportional hazard
model with frailty. We consider a regression model for the variance components in
the proportional hazards frailty model. We propose a Bayesian model averaging procedure
with a reversible jump Markov chain Monte Carlo step which selects the model
automatically. The resulting regression coefficient estimates ignore the model uncertainty
from the frailty distribution. Finally, the proposed model and the estimation
procedure are illustrated with simulated example and real data.
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Construction and parameter estimation of wrapped normal modelsRoux, Hannaline January 2019 (has links)
If a known distribution on a real line is given, it can be wrapped on the circumference
of a unit circle. This research entails the study of a univariate skew-normal distribution
where the skew-normal distribution is generalised for the case of bimodality. Both
the skew-normal and
exible generalised skew-normal distributions are wrapped onto
a unit circle, consequently referred to as a wrapped skew-normal and a wrapped
exible
generalised skew-normal distribution respectively. For each of these distributions a
simulation study is conducted, where the performance of maximum likelihood estimation
is evaluated. Skew scale mixtures of normal distributions with the wrapped version
of these distributions are proposed and graphical representations are provided. These
distributions are also compared in an application to wind direction data. / Dissertation (MSc)--University of Pretoria, 2019. / Statistics / MSc / Unrestricted
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A simulation study of the robustness of Hotelling’s T2 test for the mean of a multivariate distribution when sampling from a multivariate skew-normal distributionWu, Yun January 1900 (has links)
Master of Science / Department of Statistics / Paul I. Nelson / Hotelling’s T2 test is the standard tool for inference about the mean of a multivariate normal population. However, this test may perform poorly when used on samples from multivariate distributions with highly skewed marginal distributions. The goal of our study was to investigate the type I error rate and power properties of Hotelling’s one sample test when sampling from a class of multivariate skew-normal (SN) distributions, which includes the multivariate normal distribution and, in addition to location and scale parameters, has a shape parameter to regulate skewness.
Simulation results of tests carried out at nominal type I error rate 0.05 obtained from various levels of shape parameters, sample sizes, number of variables and fixed correlation matrix showed that Hotelling’s one sample test provides adequate control of type I error rates over the entire range of conditions studied. The test also produces suitable power levels for detecting departures from hypothesized values of a multivariate mean vector when data result from a random sample from a multivariate SN. The shape parameter of the SN family appears not to have much of an effect on the robustness of Hotelling’s test. However, surprisingly, it does have a positive impact on power.
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The Inverse Problem of Multivariate and Matrix-Variate Skew Normal DistributionsZheng, Shimin, Hardin, J. M., Gupta, A. K. 01 June 2012 (has links)
In this paper, we prove that the joint distribution of random vectors Z 1 and Z 2 and the distribution of Z 2 are skew normal provided that Z 1 is skew normally distributed and Z 2 conditioning on Z 1 is distributed as closed skew normal. Also, we extend the main results to the matrix variate case.
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On the estimation and application of flexible unordered spatial discrete choice modelsSidharthan, Raghuprasad 22 February 2013 (has links)
Unordered choice models are commonly used in the field of transportation and several other fields to analyze discrete choice behavior. In the past decade, there have been substantial advances in specifying and estimating such models to allow unobserved taste variations and flexible error covariance structures. However, the current estimation methods are still computationally intensive and often break down when spatial dependence structures are introduced (due to the resulting high dimensionality of integration in the likelihood function). But a recently proposed method, the Maximum Approximate Composite Marginal Likelihood (MACML) method, offers an effective approach to estimate such models. The MACML approach combines a composite marginal likelihood (CML) estimation approach with an approximation method to evaluate the multivariate standard normal cumulative distribution (MVNCD) function. The composite likelihood approach replaces the likelihood function with a surrogate likelihood function of substantially lower dimensionality, which is then subsequently evaluated using an analytic approximation method rather than simulation techniques. This combination of the CML with the specific analytic approximation for the MVNCD function is effective because it involves only univariate and bivariate cumulative normal distribution function evaluations, regardless of the dimensionality of the problem.
For my dissertation, I have four objectives. The first is to evaluate the performance of the MACML method to estimate unordered response models by undertaking a Monte Carlo simulation exercise. The second is to formulate and estimate a spatial and temporal unordered discrete choice model and apply this model to a land use change context and to the mode choice decision of school children. The third objective is to formulate a random coefficient model with non-normal mixing distributions on model parameters which can be estimated using the MACML approach. Finally, the fourth objective us to propose an improvement to the MACML method by incorporating a second order MVNCD function that is more accurate and evaluate its performance in estimating parameters for a variety of model structures. / text
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Sequential Inference and Nonparametric Goodness-of-Fit Tests for Certain Types of Skewed DistributionsOpperman, Logan J. 07 August 2019 (has links)
No description available.
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Sequential Change-point Analysis for Skew Normal Distributions andNonparametric CUSUM and Shiryaev-Roberts Procedures Based onModified Empirical LikelihoodWang, Peiyao 23 August 2022 (has links)
No description available.
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A Novel Accurate Approximation Method of Lognormal Sum Random VariablesLi, Xue 15 December 2008 (has links)
No description available.
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An extension of Birnbaum-Saunders distributions based on scale mixtures of skew-normal distributions with applications to regression models / Uma extensão da distribuição Birnbaum-Saunders baseado nas misturas de escala skew-normal com aplicações a modelos de regressãoSánchez, Rocio Paola Maehara 06 April 2018 (has links)
The aim of this work is to present an inference and diagnostic study of an extension of the lifetime distribution family proposed by Birnbaum and Saunders (1969a,b). This extension is obtained by considering a skew-elliptical distribution instead of the normal distribution. Specifically, in this work we develop a Birnbaum-Saunders (BS) distribution type based on scale mixtures of skew-normal distributions (SMSN). The resulting family of lifetime distributions represents a robust extension of the usual BS distribution. Based on this family, we reproduce the usual properties of the BS distribution, and present an estimation method based on the EM algorithm. In addition, we present regression models associated with the BS distributions (based on scale mixtures of skew-normal), which are developed as an extension of the sinh-normal distribution (Rieck and Nedelman, 1991). For this model we consider an estimation and diagnostic study for uncensored data. / O objetivo deste trabalho é apresentar um estudo de inferência e diagnóstico em uma extensão da família de distribuições de tempos de vida proposta por Birnbaum e Saunders (1969a,b). Esta extensão é obtida ao considerar uma distribuição skew-elíptica em lugar da distribuição normal. Especificamente, neste trabalho desenvolveremos um tipo de distribuição Birnbaum-Saunders (BS) baseda nas distribuições mistura de escala skew-normal (MESN). Esta família resultante de distribuições de tempos de vida representa uma extensão robusta da distribuição BS usual. Baseado nesta família, vamos reproduzir as propriedades usuais da distribuição BS, e apresentar um método de estimação baseado no algoritmo EM. Além disso, vamos apresentar modelos de regressão associado à distribuições BS (baseada na distribuição mistura de escala skew-normal), que é desenvolvida como uma extensão da distribuição senh-normal (Rieck e Nedelman, 1991), para estes vamos considerar um estudo de estimação e diagnóstisco para dados sem censura.
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