L-Moment estimators as applied to gamma drop size distributions

The traditional approach with experimental raindrop size data is to use the method of moments (MM) in the fitting procedure to estimate the parameters for the raindrop size distribution (RSD). However, the moment method is known to be biased. Therefore, we investigated the L-moment method, which is widely used by hydrologists. We applied the L-moment method, MM and maximum likelihood (ML) methods to simulated samples taken from exponential, gamma, and lognormal raindrop populations. A comparison of the bias involved in the fitting procedures of moments, ML, and L-moments shows that ML and L-moments outperform MM, and for small sample sizes L-moments outperforms ML.

The effects of the absence of small drops in the samples (typical disdrometer minimum size thresholds are 0.3-0.5 mm) on the fitting procedures are also analyzed. Our results show that missing small drops, due to the instrumental constraint, results in a large bias in the case of the L-moment and ML fitting methods; this bias did not decrease with increasing sample size. The very small drops have a negligible effect on moments of order two or higher and the bias in the moment methods seems to be about the same as in the case of full samples.