Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities

Author:

Alanzi Ayed. R. A.1,Imran Muhammad2,Tahir M. H.2,Chesneau Christophe3,Jamal Farrukh2,Shakoor Saima4,Sami Waqas5

Affiliation:

1. Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia

2. Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan

3. Université de Caen Normandie, LMNO, Campus II, Science 3, Caen 14032, France

4. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

5. College of Nursing, QU Health, Qatar University, Doha, P.O. Box 2713, Qatar

Abstract

<abstract><p>In this article, we make mathematical and practical contributions to the Bell-X family of absolutely continuous distributions. As a main member of this family, a special distribution extending the modeling perspectives of the famous Burr XII (BXII) distribution is discussed in detail. It is called the Bell-Burr XII (BBXII) distribution. It stands apart from the other extended BXII distributions because of its flexibility in terms of functional shapes. On the theoretical side, a linear representation of the probability density function and the ordinary and incomplete moments are among the key properties studied in depth. Some commonly used entropy measures, namely Rényi, Havrda and Charvat, Arimoto, and Tsallis entropy, are derived. On the practical (inferential) side, the associated parameters are estimated using seven different frequentist estimation methods, namely the methods of maximum likelihood estimation, percentile estimation, least squares estimation, weighted least squares estimation, Cramér von-Mises estimation, Anderson-Darling estimation, and right-tail Anderson-Darling estimation. A simulation study utilizing all these methods is offered to highlight their effectiveness. Subsequently, the BBXII model is successfully used in comparisons with other comparable models to analyze data on patients with acute bone cancer and arthritis pain. A group acceptance sampling plan for truncated life tests is also proposed when an item's lifetime follows a BBXII distribution. Convincing results are obtained.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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