The Weibull-Rayleigh Distribution and Its Properties

In this paper we consider certain results characterizing the generalization of Weibull and Rayleigh distributions through their distribution functions and moment generating functions. Our work was motivated in part by a new method for generating families of continuous random variable developed in Alzaatreh et al (2013a). The resulting Weibull-Rayleigh distribution was defined and some of its properties like the moment generation function, moments, cumulants, survival function, hazard function and Shannon entropy were investigated. This distribution was found to generalize some known distributions. Simulated data were analyzed and density plots given. Results showed that the Weibull-Rayleigh distribution is highly peaked, skewed, unimodal with heavy tails. Consequently, the proposed generalized distribution can represent effectively, heavily tailed and slightly skewed and normal type distributions that are unimodal. Keywords: Weibull distribution, Rayleigh Distribution, Transformed-Transformer Family, Moments, unimodal..