Estimation of model parameters of dependent processes constructed using Lévy Copulas

Abstract

The degradations of engineering components can be dependent. This study considers that a d-dimensional subordinator constructed based on Lévy copula can be used to model the dependency. Three procedures to estimate model parameters of the process constructed based on Clayton Lévy copula with the gamma processes as marginals are investigated through simulation. The first one assumes that jumps of the processes are observable; the second one uses the increments of degradation as samples; and the third one is based on the concept of jump tail dependence coefficient. An application is presented by estimating model parameter and calculating the system reliability.

Keywords:

• Subordinator
• Lévy copula
• Dependency
• Parameter estimation
• Gamma process
• Clayton Lévy copula

Acknowledgement

The authors gratefully acknowledge their corresponding financial support from the Natural Science and Engineering Research Council of Canada (RGPIN-2016-04814 for H. P. Hong, RGPIN-2014-04710 for J. D. Ren) and from the University of Western Ontario.