The zero truncated Poisson Burr X family of distributions with properties, characterizations, applications, and validation test

摘要

The goal of this work is to introduce a new family of continuousdistributions with a strong physical applications. Some statisticalproperties are derived, and certain useful characterizations of the proposedfamily of distributions are presented. Five applications are provided toillustrate the importance of the new family. A modified goodness-of- fittest for the new family in complete data case are investigated via twoexamples. We propose, as a first step, the construction ofNikulin-Rao-Robson statistic based on chi-squared fit tests for the newfamily in the case of complete data. The new test is based on theNikulin-Rao-Robson statistic separately proposed by [M. S. Nikulin, TheoryProbab. Appl., (extbf{18}) (1974), 559--568] and [K. C. Rao, B. S.Robson, Comm. Statist., (extbf{3}) (1974), 1139--1153]. As a second step,an application to real data has been proposed to show the applicability ofthe proposed test.