Bivariate exponentiated generalized inverted exponential distribution with applications on dependent competing risks data

Ammar M. Sarhan; Rabab S. Gomaa; Alia M. Magar; Najwan Alsadat; Ammar M. Sarhan; Rabab S. Gomaa; Alia M. Magar; Najwan Alsadat

doi:10.3934/math.20241427

AIMS Mathematics

2024, Volume 9, Issue 10: 29439-29473. doi: 10.3934/math.20241427

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Research article

Bivariate exponentiated generalized inverted exponential distribution with applications on dependent competing risks data

1.
Department of Mathematics and Statistics, Dalhousie University, Canada
2.
Department of Mathematics, Mansoura University, Mansoura 35516, Egypt
3.
Department of Quantitative Analysis, College of Business Administration, KSU, P.O. Box 71115, Riyadh 11587, Saudi Arabia

Received: 20 June 2024 Revised: 16 September 2024 Accepted: 29 September 2024 Published: 17 October 2024
MSC : 62D05, 62G30, 62P99

This paper introduces a novel bivariate distribution derived from the univariate exponentiated generalized inverted exponential (EGIE) distribution, which we term the bivariate exponentiated generalized inverted exponential (BEGIE) distribution. The newly proposed distribution belongs to the Marshall-Olkin class. Several statistical attributes of the BEGIE distribution are explored. The utility of this distribution is examined through applications on both bivariate data and dependent competing risks data. Estimation processes for the model's parameters, using maximum likelihood and Bayesian methods, are outlined for scenarios involving both bivariate and dependent competing risks data. Due to the absence of closed-form solutions for these estimators, numerical optimization techniques are employed. Furthermore, the proposed distribution is illustrated and evaluated through the analysis of three real datasets: two involving bivariate data, and the other involving dependent competing risks data.
- reliability analysis,
- statistical inferences,
- Bayesian analysis,
- shock models
Citation: Ammar M. Sarhan, Rabab S. Gomaa, Alia M. Magar, Najwan Alsadat. Bivariate exponentiated generalized inverted exponential distribution with applications on dependent competing risks data[J]. AIMS Mathematics, 2024, 9(10): 29439-29473. doi: 10.3934/math.20241427

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Abstract

This paper introduces a novel bivariate distribution derived from the univariate exponentiated generalized inverted exponential (EGIE) distribution, which we term the bivariate exponentiated generalized inverted exponential (BEGIE) distribution. The newly proposed distribution belongs to the Marshall-Olkin class. Several statistical attributes of the BEGIE distribution are explored. The utility of this distribution is examined through applications on both bivariate data and dependent competing risks data. Estimation processes for the model's parameters, using maximum likelihood and Bayesian methods, are outlined for scenarios involving both bivariate and dependent competing risks data. Due to the absence of closed-form solutions for these estimators, numerical optimization techniques are employed. Furthermore, the proposed distribution is illustrated and evaluated through the analysis of three real datasets: two involving bivariate data, and the other involving dependent competing risks data.

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