Harmonic Extensions of Gompertz, Frechet And Burr ´ XII Distributions with Applications to Lifetime Data

Abstract

This thesis aims to enhance the modelling capabilities of the Gompertz, Fr´echet, and Burr XII distributions using the harmonic mixture G family. These classical distributions are widely used in various fields to represent different types of data, but they often face limitations in capturing complex data characteristics such as skewness and heavy tails. To achieve this objective, the research utilises the harmonic mixture G family as generator to modify the Gompertz, Fr´echet, and Burr XII distributions. The modified distributions are then evaluated using the maximum likelihood estima tion, ordinary least squares, weighted least squares, Cram´er-von Mises, and Anderson Darling estimation methods to estimate their parameters. Monte Carlo simulation ex periments were performed to identify the best estimation methods for the parameters. The maximum likelihood estimation method was adjudged the best estimator for the models developed. Additionally, parametric regression models were developed based on two of these modified distributions, providing a framework for analysing relationships between variables. The findings of this research demonstrate that integrating the harmonic mixture G family significantly enhances the modelling capabilities of the Gompertz, Fr´echet, and Burr XII distributions. The modifications enable these distributions to better capture skewness and heavy tails, leading to a more accurate representation of real-world data patterns. The developed parametric regression models further enhance the flexibility and versatility of these modified distributions, facilitating improved analysis of complex relationships. The practical implications of this research are extensive, benefiting various fields such as finance, economics, environmental sciences, engineering, and risk analysis. Researchers and practitioners can leverage the modified distributions and parametric regression models to more effectively model and analyse complex data patterns, enabling improved decision-making, risk assessment, and predictive modelling.