# On the hypergeometric distribution

1. Apr 23, 2015

While I do understand the story of the hypergeometric distribution, I was wondering if there's anything "geometric" about it, or if there's any connection between the distribution and "geometry". Can anyone throw some light on it?

Thanks,

2. Apr 24, 2015

### Stephen Tashi

I don't know the history, but I'll speculate that the "geometric" part comes from the use of the adjective "geometric" in "geometric series". I think a "hypergeometric series" is a generalization of the idea of a "geometric series".

3. May 8, 2015

Historically "hypergeometric" was first used for the series and differential equations. It was applied to the distribution because the probability generating function for the distribution involves a hypergeometric function. (That was the explanation provided to use many, many, many, years ago in graduate school.)

4. May 8, 2015

### micromass

That seems like the right explanation. According to wikipedia:

But why did Wallis call this series "hypergeometric"?

5. May 8, 2015

### micromass

According to the book "The words of mathematics: an etymological dictionary of mathematical terms used in english" by Steven Schwartzman, we have

And finally, here is an explanation of why geometric series were called like this: https://www.math.toronto.edu/mathnet/questionCorner/arithgeom.html

So it is funny to realize that the name for the hypergeometric distribution (which measures the probability of winning in some sot of lottery) comes from trying to find a square with the same area as a rectangle.