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A Weighting Rule and an End Point Correction for Moments of Truncated Distributions
Author(s) -
Darvell B. W.
Publication year - 1990
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347810
Subject(s) - weighting , end point , point (geometry) , mathematics , statistics , geometry , physics , acoustics
SUMMARY 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.