A Novel Three-Parameter Extended Weibull Distribution for Health Data Modelling

TL;DR

This paper introduces a new three-parameter extended Weibull distribution designed for better modeling of health data, especially in extreme tail events, with comprehensive statistical analysis and empirical validation.

Contribution

The paper proposes a novel three-parameter Weibull extension with enhanced tail flexibility, deriving its properties and demonstrating superior fit on health data compared to existing models.

Findings

The new distribution outperforms five similar Weibull extensions on fracture data.

Simulation shows maximum likelihood estimates are effective for the model.

The distribution provides a better fit for heavily tailed health data.

Abstract

Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with additional flexibility without sacrificing tractability. We derived and studied its statistical properties, including reliability measures, quantile function, moment, stress-strength, mean waiting time, moment generating function, characteristics function, R\'enyi entropy, order statistics, mean residual life and mode. We adopted the inverse transform approach in random number generation, and through simulation, we evaluated the performance of the maximum likelihood estimates. The fitness of the distribution was examined using a fracture dataset and compared with five similar extensions of the Weibull distribution. Our proposed novel distribution fits the data best among the competing models. It is therefore recommended as a better alternative in modelling heavily tailed health data due to its flexibility. Robust estimation techniques would be valuable in addressing potential numerical challenges associated with the model in future studies.