Parameter Estimation for an n-variate FGM Copula and Its Application to Dependent Failure Analysis  
Author Shuhei Ota

 
Co-Author(s) Mitsuhiro Kimura

 
Abstract In this study, we propose an estimation method of the dependence parameters of an n-variate Farlie-Gumbel- Morgenstern (FGM, for short) copula when parameters of its marginal distributions are not given. The n-variate FGM copula, one of the multivariate distribution functions, has been used to model mutual dependencies of system components. However, maximum likelihood estimation (MLE, for short) for the dependence parameters is computationally difficult or infeasible for a large number n because the FGM copula contains 2n − n − 1 dependence parameters. To solve such a problem, we break it down into simpler problems by nesting maximum likelihood estimators. Then, we estimate the dependence parameters one by one by solving these problems. Although the estimation accuracy of the proposed method is inferior to that of MLE, our method has an advantage that the estimates can be successfully obtained for any given n. Via simulation studies, the performance of the proposed method is shown.

 
Keywords Farlie-Gumbel-Morgenstern copula, multivariate distribution, mutual dependency, maximum likelihood estimation
   
    Article #:  2477
 
Proceedings ISSAT International Conference on Reliability and Quality in Design 2018
August 2-4, 2018 - Toronto, Ontario, Canada