Type II heavy tailed family with applications to engineering, radiation biology and aviation data

The study proposes the Type II Heavy-Tailed family with a particular distribution called the Type II Heavy-Tailed Weibull distribution as its extension, which has the main purpose of fitting heavy-tailed data. Special cases of the TII-HTW distribution featuring new models, namely the reduced Type II heavy-tailed Weibull (reduced TII-HTW), Type II heavy-tailed exponential (TII-HTE), and Type II heavy-tailed Rayleigh (TII-HTR) distributions, were identified for further studies. The statistical properties concerning moments and half-life along with probability density functions and other functions are derived and investigated. Some of the methods used to estimate parameters are Maximum Likelihood Estimation (MLE), Maximum Product Spacing (MPS), Least Squares (LS), Weighted Least Squares (WLS), Cramér-von Mises (CvM) and Anderson–Darling (AD), Right-Tailed Anderson–Darling, and Bayesian Estimation. To check the estimation methods, a Monte Carlo simulation has been run with the parameters being fixed initial values, which were carefully fixed to represent realistic scenarios to guarantee remaining stable and convergence of methods. The results indicate that MLE appeared to be consistent and effective; however, LS estimates and WLS and CvM estimators appeared to be reliable. Bayesian estimates seemed to have given good results with larger sample sizes. The applicability of the model against real datasets was performed, and the model showed an improved capacity in characterizing heavy-tailed behavior. The results emphasize possible applications of the distribution in reliability analysis, survival modeling, and financial risk, with suggested future research options involving high-dimensional extensions and alternative estimation methods.