New Weighted Rayleigh Version of Azzalini Distribution

Abstract

In this article a new weighted Rayleigh distribution has been proposed.  The main difference between the proposed distribution and the other existing Rayleigh families is that, usually, when families add such a parameter, it creates new behavior, such as ( tail). In the proposed distribution, the new parameter η interacts with β to adjust the spreading. It is simpler and more computationally.

The distribution's properties have been analyzed, and the maximum-likelihood method was suggested for the estimation of the parameters of the new distribution. The novel weighted distribution was exemplified through its application to an actual lifetime dataset.