Inference procedures for bivariate exponential model of Gumbel

In this article, statistical properties of an absolutely continuous bivariate exponential model due to Gumbel (1960) are examined and the Fisher information matrix is derived. Simple estimators are motivated from a structural representation of the model and are compared both in terms of asymptotic efficiency and finite sample simulation. Besides their good performance, some of the simple estimators lead to exact or nearly exact confidence interval and hypotheses test procedures. The proposed methods are illustrated by reanalyzing a data set to which asymptotic methods were employed by Gross and Lam (1981) under a different bivariate exponential model.