A new and generalized family of heavy-tailed-Topp-Leone-type II exponentiated half logistic-G distribution with applications

We develop a novel family of distributions named heavy-tailed Topp-Leone-type II exponentiated half logistic distribution. Several mathematical properties including linear representation, Rényi entropy, quantile function, probability weighted moments, and distribution of order statistics are obtained. Estimation methods including maximum likelihood estimation, Cramér-von Mises, Anderson–Darling, right-tail Anderson–Darling, ordinary least squares and weighted least squares are compared using simulation studies to identify which method is most appropriate for the new distribution. Weibull and log–logistic distributions are used as baseline distributions to demonstrate the flexibility of the density and hazard rate functions of the new family of distributions. In addition, several actuarial measures including tail value at risk, tail variance, value at risk and tail variance premium are explored and their numerical studies are conducted to verify that the new distribution is heavy-tailed. These risk measures are used in fields such as finance to compare the risk of several investment portfolios. A special model of the new distribution called heavy tailed Topp-Leone exponentiated half logistic-log logistic is used to show its usefulness in a real life health data, where it fitted covid-19 and hydrology data sets better than competing distributions based on several goodness-of-fit statistics.