Optimal Moment Estimators and Their Application in Stochastic Hydrometeorology

The "best" estimators (unbiased, minimal-variance) of absolute moments from a sample of independent realizations of a random variable are the respective sample moments. This, however, holds true, in general, only when no further information about the stochastic process involving those random variables is available. If, for instance, the probability distribution function of the random variables is known, this additional information can produce better estimators from sample moments of order "a" for absolute moments of order "b" of the random variable, with a<>b. We show theoretical examples of the above, as well as possible applications to hydrometeorological variables.