Abstract
In this article, we propose a modification of the classical Weibull distribution based on the degenerate exponential function, leading to the degenerate Weibull (DW) distribution. The proposed distribution retains the Weibull distribution as a limiting case and provides additional flexibility through the degeneracy parameter. Several mathematical and statistical properties of the proposed distribution are derived, including its survival and hazard functions, quantile function, moments, skewness, kurtosis, and entropy. The shapes of the density and hazard functions are investigated for different parameter values. Maximum likelihood and Bayesian methods are developed for parameter estimation, and their finite-sample performance is examined through a Monte Carlo simulation study under different parameter settings and sample sizes. MCMC and profile likelihood diagnostics are also considered to assess the estimation results. Finally, the proposed distribution is applied to real data sets from engineering and medical applications and compared with several competing distributions using information criteria and goodness-of-fit statistics. MCMC diagnostic measures are also employed to assess the convergence and performance of the Bayesian estimation procedure. The results indicate that the proposed distribution provides a good fit to the considered data sets and may offer improved fit compared with some competing models in particular applications.