Comparison of Estimators for Parameters of Gamma Distributions with Left-Truncated Samples

Abstract

When fitting a raindrop size distribution using a gamma model from data collected by a disdrometer, some consideration needs to be given to the small drops that fail to be recorded (typical disdrometer minimum size thresholds being in the 0.3?0.5-mm range). To this end, a gamma estimation procedure using maximum likelihood estimation has recently been published. The current work adds another procedure that accounts for the left-truncation problem in the data; in particular, an L-moments procedure is developed. These two estimation procedures, along with a traditional method-of-moments procedure that also accounts for data truncation, are then compared via simulation of volume samples from known gamma drop size distributions. For the range of gamma distributions considered, the maximum likelihood and L-moments procedures?which perform comparably?are found to outperform the procedure of method-of-moments. As these three procedures do not yield simple estimates in closed form, salient details of the R statistical code used in the simulations are included.