The maximum negative binomial distribution

被引：7

作者：

Zhang, ZX

Burtness, BA

Zelterman, D

机构：

[1] Merck Res Labs, St Petersburg 194223, Russia

[2] Yale Univ, Dept Med Oncol, New Haven, CT 06520 USA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2000年 / 87卷 / 01期

关键词：

Bernoulli distribution; negative binomial distribution; minimum negative binomial distribution; riff-shuffle distribution; coupon collector's distribution; EM algorithm;

D O I：

10.1016/S0378-3758(99)00177-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The maximum negative binomial distribution is the distribution of the smallest number of independent Bernoulli trials needed in order to observe at least c successes and c failures. This distribution arises in a design for a medical experiment. We describe the moments and modes for this distribution. When c is large there are normal and half-normal approximate distributions. If the Bernoulli parameter is extremely close to either zero or one then a gamma approximate distribution is demonstrated. Estimates of the Bernoulli parameter are described using the EM algorithm and a Bayesian prior distribution. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：1 / 19

页数：19

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