A Modified Chi-square Type Test Statistic for the Double Burr X Model with Applications to Right Censored Medical and Reliability Data

Khaoula Aidi,Mir Masoom Ali,Wahid A M Shehata,Nadeem Shafique Butt,Mohamed Ibrahim,Haitham M Yousof

doi:10.18187/pjsor.v17i3.3888

Abstract

A new modified version of the Bagdonavičius-Nikulin goodness-of-fit test statistic is presented for validity for the right censor case under the double Burr type X distribution. The maximum likelihood estimation method in censored data case is used and applied. Simulations via the algorithm of Barzilai-Borwein is performed for assessing the right censored estimation method. Another simulation study is presented for testing the null hypothesis under the modified version of the Bagdonavičius and Nikulin goodness-of-fit statistical test. Four right censored data sets are analyzed under the new modified test statistic for checking the distributional validation.

Highlights

Statistical methods for testing the validity of a parametric distribution are in increasing developments
The new type of Chisquared goodness-of-fit test statistic of Bagdonavičius-Nikulin is applied for the distributional validation under the right censored schemes
A new modified type Chi-squared goodness-of-fit test statistic which is established based on the wellknown Bagdonavičius-Nikulin test is presented and applied for distributional validation under the double

Summary

Introduction

Statistical methods for testing the validity of a parametric distribution are in increasing developments. Bagdonavičius and Nikulin (2011a,b) presented and applied a new type of Chi-squared goodnessof-fit test statistic for the censored data (right case), (see Bagdonavičius et al (2013)). The new type of Chisquared goodness-of-fit test statistic of Bagdonavičius-Nikulin is applied for the distributional validation under the right censored schemes. A new modified type Chi-squared goodness-of-fit test statistic which is established based on the wellknown Bagdonavičius-Nikulin test is presented and applied for distributional validation under the double. Burr type X (DBX) distribution model using the right censored case. The new modified Bagdonavičius-Nikulin type test is applied using four right censored real data sets for distributional validity. Following Yousof et al (2017), we construct the double Burr type X (DBX) model with CDF given by. Depending Yousof et al (2017), many auther presented and sudied new lifetime distributions (see Jahanshahi et al (2019) for the Burr X Fréchet distribution, Khalil et al (2019) for the Burr X exponentiated Weibull distribution, Abouelmagd et al (2019) for the Poisson Burr X Weibull distribution, Elsayed and Yousof (2019) for the Burr X Nadarajah Haghighi distribution, Ali et al (2021a) for odd Burr Burr X distribution and Ali et al (2021b) for the Marshall-Olkin Lehmann Burr X distribution)

Maximum likelihood estimation in censored data case

Simulations