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Biometrika 1992 79(3):651-653; doi:10.1093/biomet/79.3.651
© 1992 by Biometrika Trust
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MISCELLANEA

Interpolation rules suggested by asymptotic expansions

NIALL H. ANDERSON1, PETER HALL2 and D. M. TITTERINGTON

1Department of Statistics, University of Glasgow Glasgow G12 8QW, U.K.
2Centre for Mathematics and its Applications, Australian National University GPO Box 4, Canberra, ACT 2601, Australia
3Department of Statistics, University of Glasgow Glasgow G12 8QW, U.K.

We suggest a simple interpolation rule, based on Edgeworth and Cornish-Fisher expansions, which permits highly accurate numerical approximation in problems involving calculation of distributions or quantiles without requiring explicit calculation of terms in the expansions.

Key Words: Chi-squarcd distribution • Cornish-Fisher expansion • Cramér-von Mises statistic • Edgeworth expansion • Kolmogorov-Smirnov statistic • Linear interpolation • Quadratic interpolation • Student's t distribution


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