A FURTHER STUDY OF THE ESTIMATION OF AREA RAIN-RATE MOMENTS BY THE THRESHOLD METHOD

The mixed distribution, a mixture of the discrete mass at the origin a nd the continuous distribution, conditional on rain, is adopted as a r ain rate distribution. The kth moment of rain rate is linearly depende nt on the probability that rain rate exceeds a fixed threshold level. The paper provides an asymptotic (large-sample) property of the maximu m likelihood (ML) estimator of the proportionality constant, called sl ope. It numerically shows that the ML estimators of the slopes for the first and second moments are mutually asymptotically almost independe nt for the GATE I parameter if the thresholds are chosen to be optimal in the sense of minimizing the normalized asymptotic variances. The p roperty provides a reason why the optimal thresholds for estimating th e first and second moments of area rain rate should be used for estima ting the variance by the double threshold method. The paper also propo ses a method of choosing thresholds simultaneously for the estimation of the first and second moments of area rain rate.