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Discrete approximations to continuous univariate distributions—an alternative to simulation

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A method to replace a continuous univariate distribution with a discrete distribution that takes MN different values is analysed. Both distributions share the same rth moments for r=0, . . ., 2N−1 and their corresonding distribution functions coincide at least at M+1 points. Several statistical and engineering examples are considered in which the discrete approximation may be used to avoid a simulation study that would be much more demanding computationally.

Keywords: Exchangeable random variables; Gaussian quadrature; Moments; Orthogonal polynomials; Process capability index

Document Type: Original Article

DOI: http://dx.doi.org/10.1111/1467-9868.00180

Affiliations: University of Cantabria, Santander, Spain

Publication date: April 1, 1999

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