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Why is a negative binomial distribution just a generalized version of a geometric distribution (they are the same when r=1), while a hypergeometric distribution is like a binomial distribution without replacement?

geometric = Negative binomial when r=1 hypergeometric = binomial without replacement.

Why does it seem like 2 of the names were swapped? Wouldn't it make more sense to have the hypergeometric dist'n be a generalization of the geometric dist'n? and the negative binomial dist'n be a version of the binomial dist'n without replacement?

kjetil b halvorsen
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Sveniat
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    Distributions have been both invented and, in a sense, discovered, over several centuries. During that time there has been little or no logic to naming inventions or discoveries in any field. In fact, naming exhibits a certain perverseness: see [Stigler's Law of Eponymy](https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy) for a notable example. (Negative binomials and binomials, however, have descriptive, accurate names stemming from [Newton's Binomial Theorem](https://en.wikipedia.org/wiki/Binomial_theorem#Newton.27s_generalised_binomial_theorem).) – whuber Jul 26 '15 at 22:06
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    Following on from whuber's point, we see in an answer (also of whuber's) to a closely related question that the name 'hypergeometric' for the hypergeometric distribution also has a [logical basis](http://stats.stackexchange.com/questions/90605/why-are-the-geometric-distribution-and-hypergeometric-distribution-called-as-suc) – Glen_b Jul 26 '15 at 23:58
  • Also see [here](http://stats.stackexchange.com/questions/169109/why-is-a-negative-binomial-random-variable-called-that) for more on the negative binomial. – Glen_b Aug 28 '15 at 01:17

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Partially answered in comments:

Distributions have been both invented and, in a sense, discovered, over several centuries. During that time there has been little or no logic to naming inventions or discoveries in any field. In fact, naming exhibits a certain perverseness: see Stigler's Law of Eponymy for a notable example. (Negative binomials and binomials, however, have descriptive, accurate names stemming from Newton's Binomial Theorem.) – whuber

It should be noted though that these "descriptive, accurate" names are based on purely mathematical intuition which is maybe not natural for those of you who were unfortunate not to learn the binomial theorem from your mother when in your crib.

Following on from whuber's point, we see in an answer (also of whuber's) to a closely related question that the name 'hypergeometric' for the hypergeometric distribution also has a logical basis – Glen_b

Also see here for more on the negative binomial. – Glen_b

kjetil b halvorsen
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