All distributions should implement suitable `statistics` module traits.

[YeungOnion]

Noticed while reviewing #275 that we're missing some of the support traits (Min, Max) for multinomial. There may be others to find as well.

[soumyasen1809]

@YeungOnion I can try working on this one. if it is okay.

Also, 1 question: Minimum Value is 0, and Maximum Value is the total number of trials, n. Is my understanding correct?

[YeungOnion]

Sorry about the delay in reply,

Minimum Value is 0, and Maximum Value is the total number of trials, n.

I believe I posted the issue thinking that the above sentiment was correct. All 0 or all n, it is analogous to the impl for MultivariateNormal. However, I suppose that Max and Min for multivariate distributions are not clear.

Perhaps we could flesh out the use case of these kinds of values and then reimplement the useful trait, whether or not it maintains its name and signature. At the moment, I don't see a generic programming usage for Max and Min, i.e. I wouldn't use them as trait bounds. Further, we don't express inclusivity/exclusivity on those bounds, but I'm rambling, apologies.

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For actionable steps, I've a list below. [^obvious]

• verifying that all traits defined in statistics::traits that have an "obviously" unique implementation for a given distribution under the current constraint are implemented as such for each distribution
• enumerating instances where there are implementations of traits in statistics::traits that are not "obviously" unique
  • clearly denoting the ambiguity and the behavior chosen in the docs at the impl

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As an open question for some design, how might we reformulate this API to express something that users or contributors to statrs may wish to generically program over or use? Just to toss my own ideas into the air,

• bounds checking in pdf and cdf to test if a value is between max and min would be supported by the existing traits,
  • expressing that a value is within the sample space is possible with max and min but a notion of pdf "support" could fill the bounds checking need
• observing extreme values, like maximums or minimums from samples could be of interest as well.

Feel free to rename or open a new issue for that part as well. Thanks for your help!

[^obvious]: I use the word "obvious" to convey a very low degree of unexpectedness or very little ambiguity in behavior when a user sees the trait with it's trait level docs and sees that a given type implements it, but does not see the implementation or impl-level docs