## Monday, October 6, 2014

### Happy Birthday Holidays

Like the title asks, "How common is your birthday?" From a decade of data from 1994 to 2004, the shades of color in this display seem to indicate that September is the most common month, and further plots show that September 9, 1999 had the most births. The least common? Holidays. Perhaps the expectant parents themselves and/or health care workers keep the expectant mothers away from delivery on New Years Day, July 4th, Christmas and Christmas Eve, and several days in late November, since Thanksgiving can vary. But Leap Day, February 29th is the surely the least common. Via Visual News, via Redditer UCanDoEat.

This display brings to mind the classical birthday problem and its variations. The classical birthday problem considers the probability that in a set of n people, randomly and independently chosen, that at least one pair have the same birthday. The usual assumption is that birthdays are uniformly distributed throughout the year. The display above shows this not to be the case. Bloom(1973) in the American Mathematical Monthly showed that any non-uniform distribution of birthdays makes sharing more likely. Is is well known that for n=23 people the chances are greater than even of sharing uniformly distributed birthdays. Munford (1977) showed that this value of n=23 is also true for any non-uniform distribution. Berresford (1980) examined this with a non-uniform, data-based, distribution of birthdays, illustrating that the surprising and counter-intuitive and robust value of n=23 yields greater than even odds.