Abstract
If F1, …, Fk are multunomially distributed, then for any a1, …, ak, P(F1 ≤ a1, …, Fk ≤ ak) ≤ P(F1 ≤ a1) … P(Fk ≤ ak) For Some values of the parameters this simple upper bound is sharper than that provided by the second Bonferroni inequality. A similar result holds for the probability that F1, …, Fk all exceed certain limits.
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