A generalized Rayleigh distribution and its application

The Rayleigh distribution was introduced by Rayleigh2 and originally proposed in the fields of acoustics and optics. It has emerged as a special case of the Weibull distribution. The Rayleigh distribution has widely used in communication theory to describe hourly median and instantaneous peak power of received radio signals. Moreover, It has received a considerable attention from engineers and physicists for modeling wave propagation, radiation, synthetic aperture radar images, and other related phenomena. There have been many forms for the Rayleigh distribution to provide flexibility for modeling data. Vod3,4 proposed a powerful extension of the Rayleigh distribution and studied its properties. Its probability density function (pdf) is given by