Rainfall Drop-Size Estimators for Weibull Probability Distribution Using Method of Moments Technique

Abstract

This paper proposes a new approach for deriving the input estimators for the Weibull probability rain drop-size distribution (DSD) using the Method of Moments (MM). The Stirling's approximation is used to estimate the gamma function which is part of the raw moment function of the Weibull probability distribution. The parameters No, �� and �� are estimated using a comparative analysis with the likely measured moments of a statistical data. The new parameters are then tested with collected data at Durban, South Africa by using least squares regression fitting technique to derive their power-law relationships with rainfall rate. The results show that the proposed Weibull distribution fits well with the measured data at tested rainfall rates. In comparison with the ITU-R P. 838-3, the average RMSE of its specific attenuation is 0.99 for horizontal polarization and 1.40 for vertical polarization at selected rainfall rates for a frequency range of 0 to 100 GHz.