Transformation of Rayleigh Distribution, Properties, and Application

Abstract

The need to develop the theory of statistics and its properties follows from the fact that many types of data cannot be fitted by classical distributions. This fact invites many researchers to generate new distributions, find their properties, and implement a data set to find the best distribution that can fit the data better. In this paper, we propose special cases of Rayleigh distribution and their relationship to wellknown distributions like half-logistic distribution (HLD), generalized half-logistic distribution (GHLD), and exponentiated half-logistic distribution (EHLD). We have mainly discussed the relationship of a transformation technique of those special cases of Rayleigh distribution with different parameter values to the assigned distributions (HLD, GHLD, EHLD). We also show the mathematical statistical properties of such special cases like the rth moment, central moment, incomplete moments, the probability weighted moments, the stochastic ordering, and interval estimation within the proposed parameters. Consequently, such properties are derived to generate modern statistical characteristics related to the special cases of Rayleigh distribution. Moreover, we have set table for the calculations of particular cases with their derived moments that have previously found their theoretical representations. Finally, we set off some conclusions related to the results of this humble work.