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The error in the normal approximation to the multinomial with an increasing number of classes

✍ Scribed by Lionel Weiss

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 214 KB
Volume: 25
Category: Article
ISSN: 0894-069X
DOI: 10.1002/nav.3800250205

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✦ Synopsis

Abstract

In an earlier paper, it was shown that under certain conditions, if the number of classes in a multinomial distribution increases as the number of trials increases, the probabilities assigned to arbitrary regions by the multinomial distribution are close to the probabilities assigned by the distribution of slightly rounded‐off normal random variables. A different method of studying the approximation of the multinomial distribution by a normal distribution is to use the multivariate Berry‐Esseen bound. In this paper, these two methods are compared, particularly with respect to the class of multinomial distributions for which the bounds on the error remain useful.

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