The New Topp-Leone-Heavy-Tailed Type II Exponentiated Half Logistic-G Family of Distributions: Properties, Actuarial Measures, with Applications to Censored Data

The Topp-Leone heavy-tailed type II exponentiated half logistic-G (TL-HT-TIIEHL-G) is the newly proposed familyof distributions (FoDs) introduced in this research. The study thoroughly investigates the statistical properties ofthis FoDs, as well as its relevance in actuarial risk assessment. The estimation of the unknown model parameters is done using the method of maximum likelihood estimation, and the consistency of these estimates is assessed through the implementation of Monte Carlo simulations. Additionally, numerical simulations are conducted to analyze the risk measures associated with the TL-HT-TIIEHL-G FoDs. The Topp-Leone heavy-tailed type II exponentiated half logistic-Weibull (TL-HT-TIIEHL-W) distribution, a particular case of the TL-HT-TIIEHL-G FoDs is compared with other contending distributions including heavy-tailed distributions to evaluate its performance. The model’s capacity, adaptability, and practicality are convincingly showcased through its application to real data.