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DISTRIBUTION CHARACTERIZATION IN A PRACTICAL MOMENT PROBLEM

We investigate a problem connected with the evaluation of the asymp- totic probability distribution function (APDFs) given from a set of nite order moments by applying the Gram-Schmidt process with the aid of computer algebra. By selecting weighting (discrete or continuous) function of similar shape to desired (APDFs), orthogonal polynomial series are obtained that are stable at high order and allow accurate approximation of tail probabilities.