A Finite Mixture Three-Parameter Weibull Model for the Analysis of Wind Speed Data

This article presents a mixture three-parameter Weibull distribution to model wind speed data. The parameters are estimated by using maximum likelihood (ML) method in which the maximization problem is regarded as a nonlinear programming with only inequality constraints and is solved numerically by the interior-point method. By applying this model to four lattice-point wind speed sequences extracted from National Centers for Environmental Prediction (NCEP) reanalysis data, it is observed that the mixture three-parameter Weibull distribution model proposed in this paper provides a better fit than the existing Weibull models for the analysis of wind speed data under study.     

On the Mixture Proportional Mean Residual Life Model

In this article, we propose a new mixture model induced by the model of proportional mean residual life. Under some appropriate assumptions, it is shown that the mixing and overall variables in the model admit the positive likelihood ratio dependence structure. To see how the overall variable is affected by the stochastic variation of the mixing variable, we study some stochastic comparisons using these variables. Finally, some useful bounds for tail probability of the overall variable for large values of the mixing variable are derived.     

Size and Power of Recent Tests for Homogeneity in Exponential Mixtures

The article investigates diagnostic procedures for finite mixture models. The problem is to decide whether given data stem from an exponential distribution or a finite mixture of such distributions. Recently, three new test approaches have been proposed, the modified likelihood ratio test (MLRT) by Chen et al. (2001 Chen , H. , Chen , J. , Kalbfleisch , J. D. ( 2001 ). A modified likelihood ratio test for homogeneity in finite mixture models . Journal of the Royal Statistical Society, B 63 : 19 – 29 .[Crossref] , [Google Scholar]), the ADDS test by Mosler and Seidel (2001 Mosler , K. , Seidel , W. ( 2001 ). Testing for homogeneity in an exponential mixture model . Australian and New Zealand Journal of Statistics 43 : 231 – 247 . [Google Scholar]), and the D-test by Charnigo and Sun (2004 Charnigo , R. , Sun , J. ( 2004 ). Testing homogeneity in a mixture distribution via the l ² distance between competing models . Journal of the American Statistical Society 99 : 488 – 498 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The size and power of these tests are determined by Monte Carlo simulation and their relative merits are evaluated. We conclude that the ADDS test shows always not much less and under some alternatives, in particular lower contaminations, considerably more power than its competitors. Also, new tables for the ADDS test are provided.     

Bayesian Estimation Using Warner's Randomized Response Model through Simple and Mixture Prior Distributions

The linear discriminant function (LDF) is known to be optimal in the sense of achieving an optimal error rate when sampling from multivariate normal populations with equal covariance matrices. Use of the LDF in nonnormal situations is known to lead to some strange results. This paper will focus on an evaluation of misclassification probabilities when the power transformation could have been used to achieve at least approximate normality and equal covariance matrices in the sampled populations for the distribution of the observed random variables. Attention is restricted to the two-population case with bivariate distributions.     

Trajectory Modeling of Longitudinal Binary Data: Application of the EM Algorithm for Mixture Models

A developmental trajectory describes the course of behavior over time. Identifying multiple trajectories within an overall developmental process permits a focus on subgroups of particular interest. We introduce a framework for identifying trajectories by using the Expectation-Maximization (EM) algorithm to fit semiparametric mixtures of logistic distributions to longitudinal binary data. For performance comparison, we consider full maximization algorithms (PROC TRAJ in SAS), standard EM, and two other EM-based algorithms for speeding up convergence. Simulation shows that EM methods produce more accurate parameter estimates. The EM methodology is illustrated with a longitudinal dataset involving adolescents smoking behaviors.     

An Alternative Estimation Approach for the Heterogeneity Linear Mixed Model

In this article, an alternative estimation approach is proposed to fit linear mixed effects models where the random effects follow a finite mixture of normal distributions. This heterogeneity linear mixed model is an interesting tool since it relaxes the classical normality assumption and is also perfectly suitable for classification purposes, based on longitudinal profiles. Instead of fitting directly the heterogeneity linear mixed model, we propose to fit an equivalent mixture of linear mixed models under some restrictions which is computationally simpler. Unlike the former model, the latter can be maximized analytically using an EM-algorithm and the obtained parameter estimates can be easily used to compute the parameter estimates of interest.     

Bayesian analysis for heteroscedastic normal-Pareto mixture model with application

ABSTRACT

In this article, we propose a new distribution by mixing normal and Pareto distributions, and the new distribution provides an unusual hazard function. We model the mean and the variance with covariates for heterogeneity. Estimation of the parameters is obtained by the Bayesian method using Markov Chain Monte Carlo (MCMC) algorithms. Proposal distribution in MCMC is proposed with a defined working variable related to the observations. Through the simulation, the method shows a dependable performance of the model. We demonstrate through establishing model under a real dataset that the proposed model and method can be more suitable than the previous report.     

混合指数几何分布

本文讨论元件的寿命分布服从双参数混合指数分布,元件个数服从几何分布的情形下,定义了混合指数几何分布,并研究了该分布的各种性质,讨论了参数的极大似然估计,并使用EM算法得到参数的近似估计. 最后,本文给出了参数的渐近方差、协方差、置信区间.     

Model-based classification using latent Gaussian mixture models

A novel model-based classification technique is introduced based on parsimonious Gaussian mixture models (PGMMs). PGMMs, which were introduced recently as a model-based clustering technique, arise from a generalization of the mixtures of factor analyzers model and are based on a latent Gaussian mixture model. In this paper, this mixture modelling structure is used for model-based classification and the particular area of application is food authenticity. Model-based classification is performed by jointly modelling data with known and unknown group memberships within a likelihood framework and then estimating parameters, including the unknown group memberships, within an alternating expectation-conditional maximization framework. Model selection is carried out using the Bayesian information criteria and the quality of the maximum a posteriori classifications is summarized using the misclassification rate and the adjusted Rand index. This new model-based classification technique gives excellent classification performance when applied to real food authenticity data on the chemical properties of olive oils from nine areas of Italy.