Exponentiated Weibull Inverse Rayleigh Distribution

Abstract

This work focuses on the study of a new four-parameter Exponentiated Weibull Inverse Rayleigh Distribution (EWIR) using Exponentiated Weibull-G family of distribution as the generator. Statistical properties of the distribution (like, Moment, Quantile, Skewness & Kurtosis, Moment, Mgf) were derived along with its asymptotic behaviour. The parameters of the new distribution were estimated using Maximum Likelihood Estimation (MLE) methods. The performance of the EWIR distribution was compared with other related distribution from the literature using the Akaike Information Criterion (AIC), Bayesian information criterion (BIC), and Hannan-Quinn information criterion (HQIC) methods comparison. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations at different sample sizes. Application of the distribution was made using a real
dataset, the data set contains carbon fiber strength (20mm). The MLEs, Standard Errors (SEs), and –log-likelihood for the new distribution and five other related distributions were fitted to the data set. Goodness-of-fit measures based on AIC, BIC, Kolmogorov-Smirnov test (K-S) values and their corresponding ranks (in parentheses) for the dataset was also presented. Hence, the new EWIR model provided the best fit among the other models for the data set, since it has the lowest values of AIC, BIC, and K-S Values.