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

Ayed. R. A. Alanzi; Muhammad Imran; M. H. Tahir; Christophe Chesneau; Farrukh Jamal; Saima Shakoor; Waqas Sami; Ayed. R. A. Alanzi; Muhammad Imran; M. H. Tahir; Christophe Chesneau; Farrukh Jamal; Saima Shakoor; Waqas Sami

doi:10.3934/math.2023352

AIMS Mathematics

2023, Volume 8, Issue 3: 6970-7004. doi: 10.3934/math.2023352

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Research article

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

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

Received: 02 December 2022 Revised: 21 December 2022 Accepted: 02 January 2023 Published: 11 January 2023
MSC : 60E05, 62N05, 62F10, 62D05

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.
- Burr XII distribution,
- entropy measures,
- estimation,
- GASP,
- quality parameter,
- T-X family
Citation: Ayed. R. A. Alanzi, Muhammad Imran, M. H. Tahir, Christophe Chesneau, Farrukh Jamal, Saima Shakoor, Waqas Sami. Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities[J]. AIMS Mathematics, 2023, 8(3): 6970-7004. doi: 10.3934/math.2023352

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Abstract

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.

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