The Derived Modification of the Exponentiated Weighted Weibull Distribution

Abstract

Statistically, to retain the originality of data, appropriate probability distribution must be employed rather than transforming the existing dataset. Classical Distributions (CD) lack the ability to model and describe some important real-life events. In this study, weighted Weibull distribution (WWD) is modified using Exponentiated Weighted Weibull distribution (EWWD). The shapes of the probability density function and hazard rate functions are investigated together with some structural statistical properties of the distribution. The performances of the maximum likelihood estimation of the unknown parameters of the distribution were done by implementing the Monte Carlo simulation method. We provide applications to two datasets to prove the flexibility of the model. The processes were performed using R-software. The EWWD is considered to be more tractable and capable than the WWD. The Exponentiated weighted Weibull distribution assumes a superior performance among the compared distributions as evidenced by the Kolmogorov-Smirnov statistics and Akaike Information Criteria values.