Topp-Leone Type I Heavy-Tailed - G Power Series Class of Distributions: Properties, Risk Measures, and Applications

This study presents a new class of distributions (CoDs) called the Topp-Leone type I heavy-tailed-G power series (TL-HT-GPS),along with its subclass, the Topp-Leone type I heavy-tailed log-logistic power series (TL-HT-LLOGPS) distribution. Statistical properties of this novel CoDs were derived, and actuarial risk measures were developed and numerically simulated.The maximum likelihood estimation technique was employed to estimate the unknown parameters of the model, and Monte Carlo simulations were used to evaluate the estimates' consistency. Through the use of the Topp-Leone type I heavy-tailed log-logistic Poisson (TL-HT-LLOGP) distribution, a special case of the TL-HT-LLOGPS distribution, two real data sets including a censored case, were examined to illustrate the potential of the proposed distribution. The TL-HT-LLOGP distribution was compared to a few selected non-nested competing distributions including some known heavy-tailed distributions and power series distributions. The TL-HT-LLOGP out-performed the contending distributions through various goodness-of-fit tests conducted.