Finite Mixture Distributions with Skew Normal Components

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.