A Birthday Problem Solution for Nonuniform Birth Frequencies
A Birthday Problem Solution for Nonuniform Birth Frequencies
复制标题
出生频率不一致的生日问题解决方案
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
T. Nunnikhoven
中科院分区：
文献类型：
--
作者：
T. Nunnikhoven
在经典的生日问题中，假定出生数在全年中是均匀分布的。然而，美国的实际出生率遵循季节性模式，相对于平均每日出生频率1/365，在低于5%和高于7%之间变化。我们开发了一个递归公式的生日问题时，出生率是不均匀的，并使用它来表明，从经典的解决方案，美国出生的差异是很小的。匹配概率可以用经典解加上一系列迅速接近零的项来表示。
Abstract 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.