A Performance of Kumaraswamy Transmuted Rayleigh Distribution

Abstract

This study derived a four-parameter Kumaraswamy transmuted generalized form of Rayleigh distribution called Kumaraswamy transmuted Rayleigh distribution (KWTR) by including two-shape parameters and a transmutation parameter to the single parameter baseline Rayleigh distribution which will take care of the spread and also give a generalised distribution. The statistical properties of the proposed distribution including the shape of the distribution, hazard rate and survival function were derived. These properties were compared with the existing baseline distributions, that is, exponentiated transmuted generalized Rayleigh distribution (ETGR), transmuted generalized Rayleigh (TGR), generalized Rayleigh (GR) and Rayleigh (R) distributions. Estimates of KWTR parameters were derived by using maximum likelihood method. The performances of the distributions were compared using Akaike information criterion (AIC), Bayesian information criterion (BIC) and goodness of fit statistic contained in “fitdistrplus” of R. Two different datasets were considered.