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Biometrika 1972 59(2):303-307; doi:10.1093/biomet/59.2.303
© 1972 by Biometrika Trust
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Monotonicity properties of Dirichlet integrals with applications to the multinomial distribution and the analysis of variance

INGRAM OLKIN

Stanford University

Bounds for the tails of Dirichlet integrals are established by showing that each integral as a function of the limits is a Schur function. In particular, it is shown how these bounds apply to the simultaneous analysis of variance test and to the multinomial distribution.

Key Words: Dirichlet integrals • Simultaneous analysis of variance test • Multinomial distribution • Inequalities • Schur function • Majorization • Least favourable distribution


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