Documentation for gammavariate

The parameters of the gammavariate function (in random module) are alpha, beta.

We can see, from the mathematical description given, that these correspond to shape and scale. Wikipedia conventionally describes these using the symbols k and theta. Wikipedia uses beta for rate, which is the reciprocal of scale: beta = 1/theta

This is a proposal to:

• explain that alpha and beta are also known as shape and scale;
• reinforce that by adding that μ is proportional to scale;
• add a warning that these are not the conventional names.

or, more controversially, scrap all that and rename the parameters k and theta. I understand that the parameter names leak into the API, so maybe not this option.

Side note: there is some variability in naming convention. The only textbook i have to hand is Grimmett and Stirzaker "Probability and Random Process" (OUP, 1982). That uses Γ(λ, t) where lambda is rate and t is shape.

(A clear and concise description of the issue.)

Linked PRs

• gh-104337: Clarify random.gammavariate doc entry  #104410
• [3.11] gh-104337: Clarify random.gammavariate doc entry (GH-104410) #104481