ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIII, 1 (2004)
p. 107 114

Distribution Characterization in a Practical Moment Problem
H. C. Jimbo


Abstract.  We investigate a problem connected with the evaluation of the asymptotic probability distribution function (APDFs) given from a set of finite 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.

AMS Subject classification:  62B05, 2B99, 37C75, 37D99.  
Keywords:  Tail probabilities, problem of moments, probabilistic programming.

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