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Biometrika 1976 63(2):395-400; doi:10.1093/biomet/63.2.395
© 1976 by Biometrika Trust
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Gauss-Krawtchouk quadrature approximations for moments of multinomial type distributions

MERRITT N. SUGG and KERMIT HUTCHESON

Department of Mathematics and Computer Science, University of Arkansas Little Rock
Department of Statistics and Computer Science, University of Georgia

An algorithm is given which further simplifies the computation of certain moments defined on multinomial distributions. The algorithm is based on an application of Gaussian quadrature to summation. The statistics are linear combinations of a univariate function of the observed frequencies. The associated set of orthogonal polynomials is an extension to the set of Krawtchouk polynomials. An application to the first four momenta of the Neyman-Pearson-Wilks criterion and Shannon's index of diversity is illustrated.

Key Words: Gauss-Krawtchouk quadrature • Moments • Multinomial • Quadrature


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