A Weighting Rule and an End Point Correction for Moments of Truncated Distributions

B. W. Darvell

Journal of the Royal Statistical Society Series C, 1990, vol. 39, issue 1, 49-54

Abstract: The computation of moments of numerically defined distributions which lack analytic solutions requires estimation based on approximation rules, i.e. Riemann sums, one of the best known of which is Simpson's rule. A polynomial weighting scheme is developed which is exact for all moments of quadratic functions and which offers an improvement over Simpson's for some classes of distribution, particularly asymmetric and truncated or abruptly terminated distributions. An end point correction to the midpoint rule for truncated distributions is also derived. The weights are expressed as combinatorial functions. An application to a distribution on a circle is examined.

Date: 1990
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