نشریه اندیشه آماری
سال پانزدهم شماره 1 (پیاپی 29، تابستان 1389)

A mixture distribution is compound of two or more statistical distributions.We find a mixture distributions when the sampling is from a non-homogeneouspopulation. For example, the mixed failure time distribution of healthy and faultycomponents, weight distribution of animals with different ages or durations of cardiacpatients after surgery in different age groups will live. In this cases the curveof density function of intimacy can be multimodal in the population. Also in manycases encountered with characteristics that can set their values belong to real numbersand in fact because these characteristics usually emerge are naturally so itseems that the normal distribution is appropriate to describe them. But more studycharacteristics, we find the situation for the study population was not completelysymmetrical, and to the right or left have skewness. Thus, the variable with valuesin real numbers would be desired asymmetry. This can lead to defining the distributionof skewed-normal. Thus, at first we examine the mixture distributions and thenthe skewed-normal distribution and at the end by defining the mixture distributionwith skewed-normal components, we will find the estimations of the parameters inthis model using EM- algorithm.

In this paper it is assumed that there are k p-variate normal populationsand the aim is classification of a new p-variate observation into one of k populations.The theory and application of the Classical (non-Bayesian) approaches are availablein many multivariate text books. In This paper, following Geisser [2] and Press [6], aBayesian approach has been given for classification is introduced. Our presentationis a simpler presentation of what is available in the litrature.

This paper is devoted to computing the sample size of binomial distributionwith Bayesian approach. The quadratic loss function is considered andthree criterions are applied to obtain p-tolerance regions with the lowest posteriorloss. These criterions are: average length, average coverage and worst outcome.

In this paper, the parametric regression has been investigated. Some ofthe disadvantage are shown. Then the nonparametric regression method has beenillustrated. As two common and important nonparametric estimator, local polynomialregression and Nadaraya-Watson estimator are given.

Fuzzy linear regression models are used to obtain an appropriate linearrelation between a dependent variable and several independent variables in a fuzzyenvironment. Several methods have been proposed for evaluating fuzzy coefficientsin linear regression models. The least squares method in fuzzy linear regressionanalysis is very difficult to use directly, and hence many articles have proposed forestimating regression parameters using linear programming. In this paper, we useBootstrap method to improve the parameters of a fuzzy linear regression model.We showed that the sum of errors of the obtained estimators is significantly smallerthan that of the earlier estimates.

Lagrangian probability distributions form large class of important probabilitydistributions such as the generalized poisson, negative binomial and logarithmicseries and also power series distributions. The family of Lagrangian distributionsof the first kind are obtained from the first Lagrangian expansion and the familyof Lagrangian distributions of the second kind are obtained from the second Lagrangianexpansion. In this article, we shall first study convolution properties ofthe distributions in question and then show that the two families of Lagrangiandistributions are equivalent. Finally it is proved that some weighted distributionsof the family of the first kind Lagrangian distributions are members of the familyLagrangian distributions of the second kind.