A proposed mechanism for skewing symmetric distributions

Abstract

In this paper, we introduce a new distribution that allows us to skew any symmetric distribution which will be referred to as the deflation-inflation distribution (DID). We discuss some properties of the DID such as moments, stochastic representation, log-concavity. Also, we obtain Fisher information matrix and derive the maximum likelihood estimator of the parameters. We conduct a simulation study and use the proposed distribution to fit two data sets namely the southern oscillation index data set and the wind speed data set. We compare our findings to those based on the skewed p-generalized normal distribution as well as Azzlaini’s skew normal distribution and conclude that the DID fits both data set better then the other two approaches.