Using Simulation to Estimate Parameters for a Novel Extension Rayleigh Distribution, Properties and Failure Rate Data Application

Abstract

Simulation is necessary to indicate the superiority of methods for discriminating a particular distribution. This search was employed to illustrate the possibility of estimating the distribution parameters of a novel Generalized exponentiated Rayleigh distribution (NGERay), in several different ways Maximum Likelihood, Least Square, Weighted Least Square, Maximum Product Spacing, Anderson- Darling and Right Anderson-Darling methods. It has also been studied the statistical characteristics of the proposed distribution, including Moment, probability-weighted moments, Incomplete moments, and Quantile function. For examining the flexibility of the proposed distribution, it was compared with several previously studied distributions that have proven their flexibility in modeling failure data for various phenomena. The new distribution showed success over the rest of the aforementioned distributions, based on many criteria of conformity and suitability. The research produced encouraging results, and the researchers recommended using it to study evidence of failure, similar to the data analyzed.