In this paper, we discuss a generalization of Balakrishnan skew normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution.

We consider the problem of inference about skewness parameter in skew-normal distribution and it's difficulties. An approximately maximum likelihood estimator that is based on some prior information is proposed. Finally the efficiency of proposed estimator is assessed both theoretically and by a simulation study.

In this paper we consider several generalizations of the skew t-normal distribution, and some of their properties. Also, we represent several theorems for constructing each generalized skew t-normal distribution. Next, we illustrate the application of the proposed distribution studying the ratio of two heavy metals, Nickel and Vanadium, associated with crude oil in Shadgan wetland in the southwest of Iran at the head of the Persian Gulf.

The stochastic data envelopment analysis (SDEA) was developed considering the value of inputs and outputs as random variables. Therefore, statistical distributions play an important role in this regard. The skew-normal (SN) distribution is a family of probability density functions that is frequently used in practical situations. In this paper, we assume that the input and output variables are skew-normally distributed. With introducing asymmetric error structure for random variables of SN distribution, a stochastic BCC model is provided. The proposed model includes BCC model assuming a normal distribution of data as well. Finally, the proposed model is used in a numerical example.