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.

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.