On the hypergeometric distribution

[madhavpr]

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,
Madhav

 

[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".

 

[statdad]

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.)

 

[micromass]

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.)

That seems like the right explanation. According to wikipedia:

The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum.

But why did Wallis call this series "hypergeometric"?

 

[micromass]

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

hypergeometric ( adjective): from Greek -derived hyper- "over, beyond," and geometric (qq. v.) A hypergeometric series is so named because it "goes beyond" the complexity of a simple geometric series.

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.