Chapter 8: Gamma Rayleigh Distribution: Properties and Application

In this paper we have successfully defined a three parameter Gamma Rayleigh distribution based on T-X family of distribution introduced by Alzetreeh et al (2012). Properties including moments, mgf, and harmonic mean are studied. Also the entropy estimation of proposed Distribution is carried out. The parameters involved in the distribution are estimated by maximum likelihood method. The flexibility of this model is illustrated by means of three real life data sets and it is evident that the Gamma Rayleigh distribution provides better fit than Inverse Rayleigh distribution.