CHANGE: integer support for the Poisson distribution

[tspooner]

Summary

The latest version of rand_distr implements the Poisson distribution using num_traits to generalise across floating point value outputs. However, the definition of the Poisson distribution (see, e.g., https://en.wikipedia.org/wiki/Poisson_distribution) has an integer support. This has downstream issues for various numerical and scientific computing applications.

Details

This change would replace Float + FloatConst with, e.g., PrimInt + Unsigned to align correctly with the formal specification.

Motivation

In various scientific computing applications, one needs to generate Poisson random samples. For example, in finance, we use Poisson distributions to simulate the size of incoming orders, the number of events that occurred in a fixed window, etc etc... The current implementation, however, does not neatly support this. Indeed, it's not entirely clear how one recovers an integer value from the output without casting, which may be lossy in some instances.

Alternatives

It's unclear why the choice was made to move from natural numbers to floats. I may very well be missing something entirely here, but some documentation at the very least would be useful to aid users in correct casting into integer values.

To be clear, I'm sure there is a good reason, but if that could be cleared up it would be immensely useful.

Thanks,
Thomas

[tspooner]

My apologies, I can see that there is an existing issue on this topic. I will close.