Some Expansions to The Weibull Distribution Families with Two Parameters: A Review

Abstract

This study is concerned with reviewing the different expansions of the two parameters Weibull distribution families, which are considered popular probability distributions used in many fields, such as reliability analysis, systems engineering, and fault studies. The research aims to provide a comprehensive review of the scientific literature related to these expansions, focusing on the theoretical frameworks, practical applications, and limitations facing each type of these expansions. The main points of this study are summarized in a mathematical review of methods by which the expansions were developed to improve their suitability to various data and discussing the improvements that were added to address the problems that arise when applying the traditional version of the distribution. Integrating these expansions with the exponential distribution as a baseline to discuss the performance of each expansion, a Monte Carlo simulation was presented for each expansion and choose the best expansion using some criteria this is to calculate the efficient of estimating parameters for each expansion. As for the practical application on real data, these expansions were applied to real data  to decide the issues of performance accuracy in practical application, and compare the performance between different expansions using measures such as statistical accuracy and ease of interpretation.