A New Two-Parameter Half-Cauchy Modified Extended Exponential Distribution: Simulation, and Application to Fatigue Life Data

Abstract

This study introduces a simplified two-parameter type of the Half-Cauchy Modified Extended Exponential (HCME) distribution derived by modifying the half-Cauchy distribution and exponential distribution, leading to a more flexible lifetime distribution. We describe its statistical properties, including the probability density function, hazard function, and quantiles. A stable numerical implementation is used to estimate the parameters by maximum likelihood. The model is applied to a classical fatigue life dataset comprising 101 aluminum coupons (Birnbaum & Saunders, 1969). A simulation study is used to examine the finite-sample performance of the maximum likelihood estimators. The new HCME model exhibits an excellent fit with a Kolmogorov–Smirnov p-value of 0.945 and outperforms the three-parameter HCEE, classical Gamma, Weibull, and Lognormal distributions based on the Akaike information criterion (AIC = 915.61). The simulation study indicates that the estimators approach their true values as the sample size increases. The proposed HCME model is an important addition to lifetime modeling, especially when a fast-increasing hazard rate is anticipated, with potential applications in mechanical engineering, material science, and quality control.