A Novel Bivariate Generalized Weibull Distribution with Properties and Applications

Abstract

Univariate Weibull distribution is a well known lifetime distribution and has been widely used in reliability and survival analysis. In this paper, we introduce a new family of bivariate generalized Weibull (BGW) distributions, whose univariate marginals are exponentiated Weibull distribution. Different statistical quantiles like marginals, conditional distribution, conditional expectation, product moments, correlation and a measure component reliability are derived. Various measures of dependence and statistical properties along with aging properties are examined. Further, the copula associated with BGW distribution and its various important properties are also considered. The methods of maximum likelihood and Bayesian estimation are employed to estimate unknown parameters of the model. A Monte Carlo simulation and real data study are carried out to demonstrate the performance of the estimators and results have proven the effectiveness of the distribution in real-life situations.

KEYWORDS AND PHRASES:

• Bivariate distribution
• copulas
• exponential distribution
• inference
• Markov chain Monte Carlo
• measures of association
• Weibull distribution

MATHEMATICS SUBJECT CLASSIFICATION 2020:

• 62E15
• 62H10
• 60E05
• 62H05

Acknowledgements

The authors are thankful to the editors and anonymous referees for their constructive and helpful comments which have significantly improved the article. Dr. Ashok Kuumar Pathak would like to thank Science and Engineering Research Board, DST, Government of India [MATRICS Grant: MTR/2022/000796] for providing financial support. Dr. M. Arshad would like to thank Science and Engineering Research Board, DST, Government of India [MATRICS Grant: MTR/2018/000084] for providing financial support.

Disclosure statement

No potential conflict of interest was reported by the author(s).