Closed-form and bias-corrected estimators for the bivariate gamma distribution

Abstract

The multivariate gamma distribution has attracted increasing attention in various studies. New MLE-like estimators in closed form are proposed for the three parameters of the bivariate gamma distribution by applying the likelihood function of a transform of the bivariate gamma variable. The MLE-like estimator of the scale parameter is equal to its maximum likelihood estimator (MLE) and method of moment estimator (MME) when the estimated values of the two shape parameters are identical. In large samples, strong consistency and asymptotic normality of the MLE-like estimators are confirmed. Based on the MLE-like estimator and the MLE, two types of bias-corrected estimators (BC-MLE and BC-MLL estimators) are developed to reduce the bias in small samples. These two estimators are asymptotically unbiased. Simulation studies suggest that MLE-like estimators have a performance similar to that of the MLE. The BC-MLE and BC-MLL estimators significantly improve the small-sample performance.