On Wednesday, 30 November 2016 at 21:12:16 UTC, Ilya Yaroshenko wrote:
"random distribution" is like "accidental distribution".

Not really.  I would use "randomly chosen distribution" for that.

"random variable" is much more frequently used definition is stats world (stats world != stats packages). Also this better describes what functionality provides module. "Distribution" may be used for PDF or for CDF (or their pair). "probability distribution" and "random variable" looks better (IMHO) then "random distribution", which has another meaning in stats world: a distribution, which was chosen randomly from a class of distributions. For example, variance-mean mixtures. --Ilya

"Random variable" is obviously the strict mathematical term, but there are a few reasons why "distribution" might be a better term to use in the API:

* many users will not be statisticians; "distribution" is likely to be a more easily-understood term, while "variable" may confuse some users since it may be mixed up with 'variable' as in a program variable;

* outside of mathematics many researchers use the term "distribution"
    quite casually and readily;

* the C++11 standard calls these entities distributions, so calling the D functionality by similar names allows for easy understanding and

(Strictly speaking the C++11 standard uses 'distribution' to refer to functors that take a source of uniformly-distributed random bits as input, and use that to generate variates with other statistical properties.)

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