Rayleigh-Rayleigh Distribution: Properties and Applications

Abstract

In this paper, a new compound distribution named Rayleigh-Rayleigh (Ra-Ra) is presented. Several structural statistical properties of new distribution containing explicit expressions for the r-th moments, characteristic function, quantile function, order statistics, Shannon and relative entropies, besides stress strength reliability were considered and studied. The unknown parameters of Ra-Ra distribution have been estimated under the maximum likelihood estimation method. Moreover, the Ra-Ra distribution is applied upon a simulation study and real data set in order to evaluate its utility and flexibility.