The New Family of Exponentiated Half Logistic-Type I Heavy-Tailed-G Distributions with Applications

In this research, we present and examine the exponentiated half logistic-type I heavy-tailed-G (EHL-TIHT-G) family of distributions (Fod). Properties and characteristics of this newly proposed Fod are investigated. Moments, stochastic ordering, order statistics, and R'enyi entropy were derived. To estimate the parameters of the EHL-TIHT-G distribution, we used seven estimation methods and a Monte-Carlo simulation exercise to evaluate the performance of the parameter estimates. The simulation investigation showed that the maximum likelihood estimates (MLEs) were the best for this model. We also derive actuarial risk measures and look at their numerical simulations. Finally, we demonstrate the practical usefulness of the HL-TIHT-G Fod through two real data examples. Our results suggest that the EHL-TIHT-G distribution can serve as a flexible and valuable model for a variety of applications.