USING FINITELY ADDITIVE PROBABILITY - UNIFORM DISTRIBUTIONS ON THE NATURAL-NUMBERS
成果类型：
Article
署名作者：
KADANE, JB; OHAGAN, A
署名单位：
University of Nottingham
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.2307/2291075
发表日期：
1995
页码：
626-631
关键词：
摘要：
In the usual, countably additive definition of probability, it is not possible to have a distribution giving equal probabilities to every one of the natural numbers. Yet such a distribution would be interesting and potentially useful. This article considers an approach to this problem based on finitely additive probability. We give a necessary and sufficient condition for when specifications of the probabilities of an arbitrary collection of subsets of a space Omega can be extended to define a finitely additive probability on all the subsets of Omega. This is applied to probability statements modeling the uniform distribution on the natural numbers, using relative frequencies and residue classes to make precise notions of uniformity. Tight bounds are given on the possible values of the probability of an arbitrary set under both interpretations. These bounds are applied to several sets of interest.