Generalized Topp- Leone Distribution as a Contribution to a Semi-Parametric Family of Distributions

In this paper, the generalized Topp-Leone distribution (T-L) is proposed as a member of a semi parametric family of distributions. Quantile, mode, moments, stochastic ordering, order statistics and moments of both order statistics and joint order statistics are discussed. The maximum likelihood estimation method is considered. To evaluate the study's results, simulation issues are provided and two real data sets are reanalyzed. Moreover, a bivariate extension of this distribution named bivariate generalized Topp-Leone (BGT-L) is introduced. The proposed bivariate version is of type Farlie–Gumbel–Morgenstern (FGM) copula. The BGT-L distribution has generalized Topp-Leone marginals. The joint cumulative distribution function, the joint survival function, and the joint probability density function are also derived in compact forms. Maximum likelihood and inference functions for margins methods are used to estimate the bivariate model’s unknown parameters. Finally, we illustrate the importance of the proposed bivariate model using a real data set in the medical field