On The Inference of P(X > Y) for Clayton Copula - Frequentist Approach

By : Ashit Baran Aich

Page No: 146-159

Abstract:
In this article, we propose estimates of the reliability 𝑹=𝑷(𝑿>𝒀) which arises in a Stress-Strength (SS) model. Here, 𝑿 is the strength of a component and 𝒀 the stress under which it performs its intendedtask.Thecomponentworkseffectivelyaslong as 𝑿 remains larger than 𝒀. The problem has been studied both under parametric and non-parametric frameworks by the researchers for a long time now. In the present study, we assume 𝑿 and 𝒀 to be dependent random variables following jointly a bivariate Archimedean copula, namely, the Clayton copula where the margins are normal. An integral representation of 𝑹 is derived and evaluated numerically. Estimates of 𝑹 are suggested by (a) a moment-type estimator based on simulation, (b) Kendall’s tau, (c) Blomqvist’s beta, and (d) the methodofmaximumlikelihood.Theasymptoticproperties of these estimates are indicated. Finally, hypothesis tests concerning the Clayton copula parameter 𝜽 and 𝑹 have been discussed.

Author
Ashit Baran Aich: Formerly of Presidency College, Kolkata and Netaji Subhas Open University, Kolkata, 
 

DOI: https://doi.org/10.32381/IAPQRT.2026.50.02.2