Inferences on the Association Parameter in Farlie-Gumbel-Morgenstern Copula Based Bivariate Distribution with Application to Water Quality Data

Accepted - November 2024

Abstract

This paper focuses on the inferential aspects of the association parameter based on a random sample from a bivariate distribution which combines two marginal distributions using the Farlie-Gumbel-Morgenstern Copula (FGMC).  To best of our knowledge, most of the applications of the copula-based joint distributions use the maximum likelihood estimator (MLE) of the association parameter. But our extensive investigation on the FGMC shows, among other things, that the performance of the MLE is far from satisfactory, and Bayes estimators under suitable noninformative priors do provide substantially better performance. Therefore, this work of ours injects a new lease of life on FGMC-based joint distribution which can be used as a template to study joint distributions emerging out of other copulas. Further, it has been demonstrated how the FGMC based bivariate distribution can be used to model Arsenic contamination in groundwater in the presence of other elements.