Abstract

This article presents a comprehensive study of the transmuted Weibull-Rayleigh distribution introduced by Yahaya and Ieren (2017) using Quadratic Rank Transmutation Map proposed by Shaw and Buckley (2007). The study comprises existing and new Mathematical and Statistical properties of the transmuted Weibull-Rayleigh distribution as contained in Yahaya and Ieren (2017). Most importantly, this paper unlike the first has considered two real life datasets to check for the performance of the transmuted Weibull-Rayleigh distribution and which the outcome indicates that the introduction of the transmuted parameter has added greater skewness and flexibility to the original Weibull-Rayleigh distribution which made it to fit the two datasets better than the Weibull-Rayleigh distribution and even the conventional Rayleigh distribution.

Key words: Quadratic rank transmutation map; Transmuted Weibull-Rayleigh distribution, Model Validity, Properties, Maximum likelihood estimation; Order statistics; Survival function; Entropy; Weibull-Rayleigh distribution, Applications.