Inferences on The Standard Skew-Normal Distribution

Abstract

It is a common practice among applied researchers to assume normal distribution for naturally occurring data over the real line. But often one is not sure about the assumption of normality for various reasons, including the fact that the standard goodness of fit tests are not effective enough always, especially for small sample sizes. In such a scenario one would be better off by starting with a more versatile skew-normal distribution which is defined over the whole real line, and is a natural generalization of the usual normal distribution. This paper deals with the standard skew-normal distribution which can reduce to the standard normal distribution if the skew parameter takes the value zero. Depending on the value of the skew parameter, the standard skew-normal distribution can be either positively skewed, symmetric (standard normal), or negatively skewed. This paper is devoted to various estimation and hypothesis testing methods for the skew parameter which, to the best of our knowledge, is the first comprehensive work in this direction.