The asymptotic distribution of the maximum absolute standardized frequencies of the multinomial distribution
type: Item
instance of: scholarly article
title: The asymptotic distribution of the maximum absolute standardized frequencies of the multinomial distribution
zbMATH Open document ID: 0551.62011
author: N. E. Zubov
published in: Metron
publication date: 1983-01-01T00:00:00Z
review text: The paper presents some numerical and analytical results concerning the asymptotic distribution of the maximum absolute standardized frequencies (m.a.s.f.) of the multinomial distribution. The first part of the paper describes the numerical evaluation of the cumulative distribution function of the m.a.s.f. and suggests a conjecture on the symmetric case. The second part finds out 3 upper bounds for the quantiles of the m.a.s.f. distribution based respectively on the chi-square distribution, on the Bonferroni inequality and on an inequality due to \textit{Z. Šidak} [J. Am. Stat. Assoc. 62, 626-633 (1967; Zbl 0158.177)]. Such upper bounds are then compared with each other. Finally some simultaneous confidence intervals for multinomial proportions are presented and compared with those proposed by \textit{C. P. Quesenberry} and \textit{D. C. Hurst} [Technometrics 6, 191-195 (1964; Zbl 0129.326)] and \textit{L. A. Goodman} [ibid. 7, 247-254 (1965; Zbl 0131.177)].
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 3878149
zbMATH Keywords: maximum absolute standardized frequencies
zbMATH Keywords: multinomial distribution
zbMATH Keywords: upper bounds for the quantiles
zbMATH Keywords: chi-square distribution
zbMATH Keywords: Bonferroni inequality
zbMATH Keywords: simultaneous confidence intervals
zbMATH Keywords: multinomial proportions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3878149