Poisson generalized Rayleigh distribution with properties and application

Abstract

In this study, we have established a new three-parameter Poisson generalized Rayleigh distribution using the Poisson-Generating family of distribution. Some important mathematical and statistical properties of the proposed distribution including probability density function, cumulative distribution function, reliability function, hazard rate function, quantile, median, the measure of skewness, and kurtosis are presented. The parameters of the new distribution are estimated using the maximum likelihood estimation (MLE) method, and constructed the asymptotic confidence intervals also the Fisher information matrix is derived analytically to obtain the variance-covariance matrix for MLEs. All the computations are performed in R software. The capability and applicability of the proposed distribution is exposed by using graphical methods and statistical tests considering a real dataset. We have empirically verified that the Poisson generalized Rayleigh distribution provided a better fit and more flexible in comparison with some selected lifetime distributions.