Improved Estimation of the Correlation Coefficient in a Bivariate Exponential Distribution

Abstract

There are many forms of bivariate exponential distributions in the literature; see, for example, the recent book by Kotz, Balakrishnan and Johnson (2000). One of the known ones is the so-called Downton's bivariate exponential distribution. In the first part of the talk, I will introduce this bivariate exponential distribution. Then, I will present some of the existing methods of estimating the correlation coefficient of this bivariate exponential distribution. These estimators are highly biased particularly when the correlation in the model is high. I will then discuss two bias-reduced estimators for the correlation coefficient. I will present some Monte Carlo simulations comparing the performance of all the estimators. Next, I will suggest the use of jackknife method in order to reduce the bias of all these estimators. The bias and mean square errors of all the estimators will then be evaluated for various sample sizes and choices of the correlation coefficient. Based on these results, I will make some recommendations.