In this article we introduce a new three parameter skewed distribution of which normal distribution is a special case. This distribution is obtained by using geometric sum of independent identically distributed normal random variables. We call this distribution as the geometric skew normal distribution. Different properties of this new distribution have been investigated. The probability densit...

In this paper, we introducte a family of univariate Birnbaum-Saunders distributions arising from the skew-normal-t  distribution. We obtain several properties of this distribution such as its moments, the maximum likelihood estimation procedure via an EM-algorithm and a method to evaluate standard errors using the EM-algorithm. Finally, we apply these methods to a real data set to demonstr...

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, standardized marginal distributions are standard normal. The copula itself depends on familiar skewing construction based normal function. This concerned with two topics. First, number extensions Notably these include case in Student’s t, different degrees freedom allowed for each margin. I...

In this paper, we compute doubly truncated moments for the selection elliptical class of distributions, including some multivariate asymmetric versions well-known such as normal, Student’s t, slash, among others. We address members family, establishing neat formulation high-order and its first two moments. establish sufficient necessary conditions existence these Further, propose optimized meth...

The stochastic data envelopment analysis (SDEA) was developed considering the value ofinputs and outputs as random variables. Therefore, statistical distributions play an importantrole in this regard. The skew-normal (SN) distribution is a family of probability densityfunctions that is frequently used in practical situations. In this paper, we assume that the inputand output variables are skew-...