The extended Burr-R class: properties, applications and modified test for censored data

Abdulhakim A. Al-Babtain; Rehan A. K. Sherwani; Ahmed Z. Afify; Khaoula Aidi; M. Arslan Nasir; Farrukh Jamal; Abdus Saboor; Abdulhakim A. Al-Babtain; Rehan A. K. Sherwani; Ahmed Z. Afify; Khaoula Aidi; M. Arslan Nasir; Farrukh Jamal; Abdus Saboor

doi:10.3934/math.2021176

AIMS Mathematics

2021, Volume 6, Issue 3: 2912-2931. doi: 10.3934/math.2021176

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Research article

The extended Burr-R class: properties, applications and modified test for censored data

1.
Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia
2.
College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Pakistan
3.
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt
4.
Laboratory of probability and statistics LaPS, University Badji Mokhtar-Annaba, Algeria
5.
Government S. E College Bahawalpur, Punjab, Pakistan
6.
Department of Statistics, The Islamia University Bahawalpur, Bahawalpur, Pakistan
7.
Kohat University of Science and Technology, KPK, Pakistan

Received: 24 October 2020 Accepted: 29 December 2020 Published: 08 January 2021
MSC : 60E05, 62F10

This article introduces a new three-parameter Marshall-Olkin Burr-R (MOB-R) family which extends the generalize Burr-G class. Some of its general properties are discussed. One of its special models called the MOB-Lomax distribution is studied in detail for illustrative purpose. A modified chi-square test statistic is provided for right censored data from the MOB-L distribution. The model parameters are estimated via the maximum likelihood and simulation results are obtained to assess the behavior of the maximum likelihood approach. Applications to real data sets are provided to show the usefulness of the proposed MOB-Lomax distribution. The modified chi-square test statistic shows that the MOB-Lomax model can be used as a good candidate for analyzing real censored data.
- censored data,
- Lomax distribution,
- maximum likelihood estimation,
- modified chi-squared test,
- order statistics
Citation: Abdulhakim A. Al-Babtain, Rehan A. K. Sherwani, Ahmed Z. Afify, Khaoula Aidi, M. Arslan Nasir, Farrukh Jamal, Abdus Saboor. The extended Burr-R class: properties, applications and modified test for censored data[J]. AIMS Mathematics, 2021, 6(3): 2912-2931. doi: 10.3934/math.2021176

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Abstract

This article introduces a new three-parameter Marshall-Olkin Burr-R (MOB-R) family which extends the generalize Burr-G class. Some of its general properties are discussed. One of its special models called the MOB-Lomax distribution is studied in detail for illustrative purpose. A modified chi-square test statistic is provided for right censored data from the MOB-L distribution. The model parameters are estimated via the maximum likelihood and simulation results are obtained to assess the behavior of the maximum likelihood approach. Applications to real data sets are provided to show the usefulness of the proposed MOB-Lomax distribution. The modified chi-square test statistic shows that the MOB-Lomax model can be used as a good candidate for analyzing real censored data.

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