A Birthday Problem Solution for Nonuniform Birth Frequencies
作者:
ThomasS. Nunnikhoven,
期刊:
The American Statistician
(Taylor Available online 1992)
卷期:
Volume 46,
issue 4
页码: 270-274
ISSN:0003-1305
年代: 1992
DOI:10.1080/00031305.1992.10475901
出版商: Taylor & Francis Group
关键词: Discrete uniform distribution;Matching problem;Occupancy problem
数据来源: Taylor
摘要:
In the classical birthday problem it is assumed that the distribution of births is uniform throughout the year. Actual United States births, however, follow a seasonal pattern varying between 5% below and 7% above, relative to the average daily frequency of 1/365. We develop a recursive formula for the birthday problem when birthrates are not uniform and use it to show that the difference from the classical solution, for U.S. births, is small. The match probability can be written in terms of the classical solution plus a series of terms which rapidly approach zero.
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