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

Volume 12, Issue 5, pp 314--336 http://dx.doi.org/10.22436/jnsa.012.05.05

Publication Date: January 05, 2019 Submission Date: September 14, 2019 Revision Date: October 05, 2019 Accteptance Date: November 17, 2019

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Authors

T. H. M. Abouelmagd - Management Information System Department, Taibah University, Saudi Arabia. Mohammed S. Hamed - Management Information System Department, Taibah University, Saudi Arabia. G. G. Hamedani - Department of Mathematics, Statistics and Computer Science, Marquette University, USA. M. Masoom Ali - Department of Mathematical Sciences, Ball State University, Muncie, USA. Hafida Goual - Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria. Mustafa C. Korkmaz - Department of Measurement and Evaluation, Artvin Coruh University, Artvin, TURKEY. Haitham M. Yousof - Department of Statistics, Mathematics and Insurance, Benha University, Egypt.

Abstract

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-of- fit 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-Rao-Robson statistic separately proposed by [M. S. Nikulin, Theory Probab. Appl., \(\textbf{18}\) (1974), 559--568] and [K. C. Rao, B. S. Robson, Comm. Statist., \(\textbf{3}\) (1974), 1139--1153]. As a second step, an application to real data has been proposed to show the applicability of the proposed test.

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Keywords

• Validation test
• maximum likelihood estimation
• generating function
• moments
• zero truncated Poisson

MSC

•  60E05
•  62F10

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