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

The goal of this work is to introduce a new family of continuous distributions with a strong physical applications. Some statistical properties are derived, and certain useful characterizations of the proposed family of distributions are presented. Five applications are provided to illustrate the importance of the new family. A modified goodness-offit test for the new family in complete data case are investigated via two examples. We propose, as a first step, the construction of Nikulin-Rao-Robson statistic based on chi-squared fit tests for the new family in the case of complete data. The new test is based on the Nikulin-RaoRobson statistic separately proposed by [M. S. Nikulin, Theory Probab. Appl., 18 (1974), 559–568] and [K. C. Rao, B. S. Robson, Comm. Statist., 3 (1974), 1139–1153]. As a second step, an application to real data has been proposed to show the applicability of the proposed test.