A new family of skewed slash distributions generated by the normal kernel

Abstract

The present paper is a generalization of the recent paper by Nadaraja and Kotz (2003) (Skewed distributions generated by the normal kernel, “Statistics & Probability Letters’’, 65, pp. 269-277). The new family of univariate skewed slash distributions generated by the normal kernel arises as the ratio of skewed distributions generated by the normal kernel and independent uniform power function distribution. The properties of the resulting distributions are studied. Normal, skew normal, slash (slash normal) and skew slash distributions are special cases of this new family. The normal distribution belongs to this family, since when the skewness parameter is zero and tail parameter tends to infinity the skew slash distributions generated by normal kernel reduces to the normal distribution. The slash normal family is also belongs to this family when the skewness parameter is zero. These distributions provide us alternative choices in simulation study and in particular, in fitting skewed data sets with heavy tails. We believe that the new class will be useful for analyzing data sets having skewness and heavy tails. Heavy-tailed distributions are commonly found in complex multi-component systems like ecological systems, microarray, biometry, economics, sociology, internet traffic, finance, business etc. We are working on maximum likelihood estimation of the parameters using EM algorithm and to apply our models for analysing the genetic data sets.