On Rayleigh-Exponentiated Odd Generalized-Pareto Distribution with its Applications

Abstract

In this article, we present a new Rayleigh-Exponentiated Odd GeneralizedPareto (REOGP) distribution. It is a member of Rayleigh-Exponentiated Odd Generalized-X family introduced in earlier studies. The distribution function (CDF), probability density (PDF), survival function and the hazard rate function of the new family
member were provided. Furthermore, other mathematical properties such as moments, moment generating function, quantile function, entropy and function of order statistics were derived. The model parameters were estimated using the method of maximum likelihood (MLE); after which some asymptotic confidence bounds (ACB) of the parameters were obtained via utilization of the second derivatives of the likelihood function. In order
to showcase the level of efficiency and consistency of REOGP; a Monte-Carlo simulation was conducted and it was found that, the biases, variances and the Mean Square Error (MSE) of the given parameter values approach zero as the sample size gets larger. The performance of the proposed distribution was compared (based on some real datasets) with other recent (extensions of Pareto) distributions reported in earlier studies and the results obtained indicate that, REOGP is suitable in modeling datasets having diverse shapes of hazard rate functions and at the same time it has proven itself to be competitive as it was able to outperform all the other competing distributions.