A weighted Topp-Leone G family of distributions: properties, applications for modelling reliability data and different method of estimation

Abstract

Based on the Topp-Leone distribution, we propose a new family of continuous distributions with one shape parameter called the weighted Topp-Leone family. We study some basic properties including quantile function, asymptotic, mixture for cdf and pdf, various entropies and order statistics.Then we study Lindley case as special case with more details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, three real data sets are illustration the purposes.