A Birthday Problem Solution for Nonuniform Birth Frequencies

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.