Estimators for Parameters of Drop-Size Distribution Functions: Sampling from Gamma Distributions

This work represents a continuation of the investigation reported at the October 2005 Conference on Radar Meteorology in Albuquerque, NM. We showed that the moment estimators often used to estimate the parameters for a given rain DSD (in our case a gamma function) are indeed biased. Our conclusion was that fitting parameters using the simple method of moments produces inferior results that can lead to misleading extrapolations and inferences. This triggered our interest in searching for more robust parameter-fitting techniques. We plan to show some results of two alternative approaches: 1) using the method of maximum likelihood estimate (MLE), which is asymptotically unbiased and seeks to find the parameter values of the given distribution function by maximizing the likelihood function, and 2) using the method of L-moments, which are a linear combination of the order statistics, and have the advantages of addressing the case of outlier values as well as the small droplet region, where lack of proper characterization causes problems with the method of moments as well as with MLE. Two cases for the gamma shape parameter are considered for this study: µ = 2 and µ = 5. Preliminary results show that when complete data for the small-drop region are available the MLE estimates are converging fast to the expected values as the sample size is increasing. Results of the two methods will be presented and discussed at the conference.