The new family of Ristíc-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution with applications

We propose the new Ristić-Balakrishnan-type II Topp-Leone-heavy-tailed-G distribution. Some properties are derived including linear representation of the density function, probability weighted moments, Rényi entropy and distribution of order statistics. Several estimation methods are compared via simulation studies to establish the best method for parameter estimation of the new family of distributions. Actuarial measures are discussed and numerical studies are conducted to characterise the new family of distributions as heavy-tailed and its performance is validated using real data.