DEVELOPMENT OF GOMPERTZ GENERALISED WEIBULL DISTRIBUTION: PROPERTIES AND APPLICATIONS

Abstract

This paper introduces the Gompertz Generalised Weibull (GGWeibull) distribution, a novel and flexible statistical model obtained by applying the Gompertz generator to the Weibull baseline distribution. The GGWeibull enhances modelling capabilities by accommodating a wide range of hazard shapes and tail behaviours, making it particularly well-suited for reliability and engineering data. We derive and explore its key statistical properties, including the probability density function, cumulative distribution function, survival function, hazard function, and moments. Parameter estimation is conducted via the maximum likelihood method, and the model’s performance is rigorously assessed through goodness-of-fit measures, including the loglikelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Application to the breaking stress data of carbon fibres demonstrates the clear superiority of the GGWeibull distribution over traditional models such as the Weibull, Gompertz, Exponentiated Gompertz, and Exponentiated Weibull distributions. The GGWeibull achieves the highest loglikelihood and the lowest AIC and BIC, indicating the best balance between model fit and complexity. Visual comparisons using histograms and theoretical density plots further confirm its superior fit to empirical data. We recommend the GGWeibull distribution as a robust and flexible tool for modelling failure times, material strength, and other engineering phenomena, and encourage future research to extend its application to broader fields such as biomedical survival analysis and environmental risk modelling.