Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros

Abstract

A method for fitting parameters of the gamma distribution to data containing some zero values using maximum likelihood methods is presented. The procedure is based on a conceptual model of the data having resulted from a censoring process so that the number, but not the numerical values of observations failing below a detection limit are known. For the case of precipitation data, this detection limit is related to the threshold value for reporting occurrence or nonoccurrence. The procedure is shown to provide parameter estimates that are more efficient (i.e., precise) than those obtained using the method of moments.