The asymptotic distribution of the maximum absolute standardized frequencies of the multinomial distribution (Q801415)

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)].