A New Family of Heavy-Tailed Generalized Topp-Leone-G Distributions with Application

In this article, we introduce a robust generalization of the generalized Topp-Leone-G (GEN-TL-G) family of distributions via the heavy-tailed technique. The distribution is named heavy-tailed generalized Topp-Leone-G (HT-GEN-TL-G) family of distributions. Statistical properties of the HT-GEN-TL-G family of distributions including reliability functions, quantile function, density expansion, moments, moment generating function, incomplete moments, Rényi entropy, distribution of order statistics are derived. Different estimation methods including Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cram\'er-von Mises and Maximum Product of Spacing are utilized to estimate the unknown parameters of the new distribution, and a simulation study is used to compare the results of the estimation methods. Risk measures for this distribution were also developed and finally the effectiveness of this new family of distributions was demonstrated using applications to two real data sets.