A new extension of the FGM copula with an application in reliability

Abstract

We propose a new symmetric extension of the bivariate Farlie-Gumbel-Morgenstern (FGM) copula with given marginals. The main feature of this new extension is the higher dependence level it permits between random variables. It is shown that the range of Spearman’s Rho is $[-.33,\mathrm{ }0.375].$ We use this new extension to estimate reliability in a dependent stress-strength model with an application to the Egyptian finance system.

Keywords:

• Spearman’s rho
• FGM copula
• reliability
• stress-strength model
• log-logistic distribution