The mixed distribution, a mixture of the discrete mass at the origin and the continuous distribution, conditional on rain, is adopted as a rain rate distribution. The kth moment of rain rate is linearly dependent on the probability that rain rate exceeds a fixed threshold level. The paper provides an asymptotic (large-sample) property of the maximum likelihood (ML) estimator of the proportionality constant, called slope. It numerically shows that the ML estimators of the slopes for the first and second moments are mutually asymptotically almost independent for the GATE I parameter if the thresholds are chosen to be optimal in the sense of minimizing the normalized asymptotic variances. The property provides a reason why the optimal thresholds for estimating the first and second moments of area rain rate should be used for estimating the variance by the double threshold method. The paper also proposes a method of choosing thresholds simultaneously for the estimation of the first and second moments of area rain rate.