The Epsilon-Skew Rayleigh Distribution

Abstract

In this dissertation, a new family of skew distributions is introduced and developed, the Epsilon Skew Rayleigh. The members of this family are bimodal skewed distributions with location, scale and skewness parameters. There exist two unimodal parameter cases. The distribution can be skewed or symmetric. This distribution family has many applications including population demographics, signal dynamics, ocean wave heights and hardware failure rates. The effects of the parameters are described and developed. We derive the moment generating and maximum likelihood functions, as well as the expected value, median, modes, variance, skewness and kurtosis. The properties of a random variable with this distribution family are developed. We determine the first several central and non-central moments and develop estimators for the parameters. A simulation and an application are presented, and the modeling accuracy of this family of distributions is evaluated.