The Beta‑Power Half‑Cauchy Exponential Distribution: Model Properties and an Application to Fatigue Data

Abstract

This paper introduces the Beta‑Power Half‑Cauchy Exponential (BPHCE) distribution, a new two‑parameter lifetime model derived by incorporating a power transformation into the half‑Cauchy exponential framework. The distribution offers enhanced flexibility for modeling positive data with heavy‑tailed and skewed characteristics, while retaining a closed‑form cumulative distribution function. We derive essential statistical properties including the Probability density function(pdf), Hazard Rate function(hrf), and quantile function. Parameters of the distribution are estimated using maximum likelihood. The proposed distribution is applied to the classic fatigue‑life dataset to check the practical applicability of the distribution. Model comparison based on AIC, BIC, and related criteria shows that the BPHCE distribution outperforms several competing lifetime models, such as exponentiated Weibull, generalized exponential, and Weibull distributions. The results confirm that the BPHCE is a valuable addition to the toolbox of reliability analysts, capable of effectively describing real‑world lifetime data with complex tail behavior. The generated model will be more applicable in data analysis of various field and will help the researcher in generating new probability models and applying on the real data sets available in modern real life.