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, Rényi 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.

翻译：威布尔分布广泛应用于健康数据建模，但其尾部灵活性不足常导致极端事件拟合效果欠佳。本文提出了一种在不牺牲可解性的前提下具有更高灵活性的三参数扩展威布尔分布。我们推导并研究了该分布的统计性质，包括可靠性度量、分位函数、矩、应力-强度、平均等待时间、矩母函数、特征函数、Rényi熵、次序统计量、平均剩余寿命及众数。在随机数生成中采用逆变换方法，并通过模拟评估了最大似然估计的性能。使用骨折数据集检验该分布的拟合优度，并与五种相似的威布尔扩展分布进行比较。结果表明，所提出的新型分布在竞争模型中拟合数据效果最佳。鉴于其灵活性，该分布被推荐作为重尾健康数据建模的更优替代方案。在未来的研究中，稳健估计方法将有助于解决该模型可能存在的数值挑战。