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August 2021 Inferring association from reliability functions: An approach based on copulas
B. Vineshkumar, N. Unnikrishnan Nair
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Braz. J. Probab. Stat. 35(3): 484-498 (August 2021). DOI: 10.1214/20-BJPS491

Abstract

Nair, Sankaran and John (Metron 76 (2018) 133–153) have defined and studied the properties of reliability functions in terms of copulas. In the present paper, we investigate the utility of such functions in inferring the time-dependent association of bivariate distributions. We consider the Clayton measure of association for the study. A general expression for this measure in terms of the generator of Archimedean copulas is given, and a method of finding nature of association using the generators is provided. We derive the relationship of the association measure with the ageing property of the distribution, associated with the generator. We analyze how the hazard rate of survival copulas can be utilized in studying the association between two random variables. Applications of the results in real life situations are discussed.

Acknowledgments

We thank the Editor and two anonymous referees for their valuable comments, which helped us to improve the contents of the paper.

Citation

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B. Vineshkumar. N. Unnikrishnan Nair. "Inferring association from reliability functions: An approach based on copulas." Braz. J. Probab. Stat. 35 (3) 484 - 498, August 2021. https://doi.org/10.1214/20-BJPS491

Information

Received: 1 March 2020; Accepted: 1 September 2020; Published: August 2021
First available in Project Euclid: 22 July 2021

Digital Object Identifier: 10.1214/20-BJPS491

Rights: Copyright © 2021 Brazilian Statistical Association

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Vol.35 • No. 3 • August 2021
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