Analyzing skewed data by power normal model

The skew normal distribution, proposed by Azzalini (1985, A class of distributions which include the normal. Scand J Stat 12:171–178), can be a suitable model for the analysis of data exhibiting a unimodal density having some skewness present, a structure often occurring in data analysis. It has been observed that there are some practical problems in estimating the skewness parameter for small to moderate sample sizes. In this paper we point out those problems and propose another skewed model which we call “Power normal model”. The basic structural properties of the proposed model including its reliability properties are presented. The closeness of skew normal and power normal distributions is investigated. It is shown that the proposed model has some nice properties which make it feasible to study the estimation and testing of the skewness parameter. This can be achieved by transforming the data to the exponential model which has been studied extensively in the literature.