The modified likelihood ratio test, which is based on penalized likelihood function, is usually used for testing homogeneity of the mixture models. The efficiency of this test is seriously affected by the shape of penalty function that is used in penalized likelihood function. The selection of penalty function is usually based on avoiding of complexity and increasing tractability, hence the results may be far from optimality. In this paper, we consider a more general form of penalty function that depends on a shape parameter. Then this shape parameter and the parameters of mixture models are estimated by using Bayesian paradigm. It is shown that the proposed Bayesian approach is more efficient in comparison to modified likelihood test. The proposed Bayesian approach is clearly more efficient, specially in nonidentifiability situation, where frequentist approaches are almost failed.

This paper considers the weight distributions in order to incorporating the topics related to construction of skew-symetric (skew-normal) and bimodal distributions. It discusses that many of skew-normal distributions disscussed in recent years researches can be studid in more general form along with some other interesting aspects in context of weigth distributions. Two cosiderable case of the recent years reaserches have been disscussed. It is shown that the introduced distributions in these reseaches along with all of their interesting properties can be obtain from weigth distribution perspective as only special cases.

In this  paper  the  regression analysis with finite mixture bivariate poisson response variable is investigated from the Bayesian point of view. It is shown that  the posterior distribution can not be written in a closed form due to the  complexity of the likelihood function of bivariate Poisson distribution. Hence, the full conditional posterior distributions of the parameters are computed and the Gibbs algorithm is used to sampling from posterior distributions. A simulation study is performed in order to assess the proposed Bayesian model and its efficiency in estimation of the parameters is compared with their frequentist counterparts. Also, a real example presented to illustrate and assess the proposed Bayesian model. The results indicate to the more efficiency of the  estimators resulted from Bayesian  approach than estimators of frequentist approach at least for small sample sizes.

Regression analysis is done, traditionally, considering homogeneity and normality assumption for the response variable distribution. Whereas in many applications, observations indicate to a heterogeneous structure containing some sub-populations with skew-symmetric structure either due to heterogeneity, multimodality or skewness of the population or a combination of them. In this situations, one can use a mixture of skew-symmetric distributions to model the population. In this paper we considered the Bayesian approach of regression analysis under the assumption of heterogeneity of population and a skew-symmetric distribution for sub-populations, by using a mixture of skew normal distributions. We used a simulation study and a real world example to assess the proposed Bayesian methodology and to compare it with frequentist approach.

This paper considers the Bayesian model averaging of inverse Gaussian regression models for regression analysis in situations that the response observations are positive and right-skewed. The computational challenges related to computing the essential quantities for executing of this methodology and their dominating ways are discussed. Providing closed form expressions for the interested posterior quantities by considering suitable prior distributions is an attractive aspect of the proposed methodology. The proposed approach has been evaluated via a simulation study and its applicability is expressed by using a real example related to the seismic studies. 

Many of spatial-temporal data, particularly in medicine and disease mapping, are counts. Typically, these types of count data have extra variability that distrusts the classical Poisson model's performance. Therefore, incorporating this variability into the modeling process, plays an essential role in improving the efficiency of spatial-temporal data analysis. For this purpose, in this paper, a new Bayesian spatial-temporal model, called gamma count, with enough flexibility in modeling dispersion is introduced. For implementing statistical inference in the proposed model, the integrated nested Laplace approximation method is applied. A simulation study was performed to evaluate the performance of the proposed model compared to the traditional models. In addition, the application of the model has been demonstrated in analyzing leukemia data in Khorasan Razavi province, Iran.