An extension of Rayleigh distribution and applications

In this article, we have derived a new distribution named as Rayleigh–Rayleigh distribution (RRD) motivated by the transformed transformer technique by Alzaatreh, Lee, and Famoye (2013). The statistical properties of RRD, comprising of explicit expressions for quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, measures of uncertainty, distributions of order statistics and L moments have been derived. Parameter estimation is carried out using method of maximum-likelihood estimation and Fisher information matrix is derived. The flexibility of the new distribution is assessed by applying it to four real data sets. The comparative behavior of RRD with Rayleigh distribution, Generalized Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution and Alpha Power Rayleigh distribution provided the evidence that it outperforms the other competing distributions.