A Note on Kumaraswamy Exponentiated Rayleigh distribution

Abstract

In this paper, a new four parameter continuous distribution, called the Kumaraswamy Rayleigh (KW-ER) distribution is proposed and studied. Some mathematical properties are presented and discussed, these properties involve expansions for the cumulative and density functions, skewness and kurtosis based on the quantile function and explicit expressions for the moments and generating function. The density function of the order statistics and obtain their moments are provided. An explicit expression for Renyi entropy is obtained. The method of maximum likelihood is used for estimating the distribution parameters and the observed information matrix is derived. A data set is used to illustrate the application of the new distribution.

Keywords

• Kumaraswamy exponentiated Rayleigh distribution; quantile function; moments generating function; order statistics; maximum likelihood estimation.