Some Results on the Transmuted Odd Lindley-Rayleigh Distribution

Abstract

In this article, a new distribution named “Transmuted odd LindleyRayleigh Distribution (TOLRD)” is presented. The respective definitions of its probability density function (pdf) and cumulative distribution function (cdf) using the Quadratic Rank Transmutation Map proposed by shaw et al. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics were studied. The estimation of the distribution?s parameters was conducted using the method of maximum likelihood. The performance of the proposed probability distribution, TOLRD is compared to some other generalizations of Rayleigh distribution using one real life dataset and two simulated datasets. The results obtained were compared using the values of the AIC, CAIC, BIC and HQIC of the fitted distributions and it showed that the TOLRD outperforms all the other fitted distributions.