Poisson distribution support

[krishvishal]

The λ parameter of Poisson is only defined for positive reals. But here its defined for λ >= 0.

Is this intended?

dist = Poisson(0); #no problem

dist = Poisson(-1) #ERROR: DomainError with -1.0: (as intended)

[simsurace]

What's the problem with Poisson(0)?

[krishvishal]

Poisson(0) makes the mass concentrated at zero, and turns into Dirac.

And also multiple textbooks define the rate parameter λ to be positive real.

Ref:

1. A Modern Introduction to Probability and Statistics - page 163, section11.5
2. https://en.wikipedia.org/wiki/Poisson_distribution - Definition section
3. Bertsekas and Tsitisklis - Section 2.3

[simsurace]

Sure, if you want a proper (non-degenerate) Poisson distribution, you have to choose a positive parameter, but the same could be said about many other distributions, e.g. Bernoulli(p)as p->0. Many of those have limits (edge cases) which are still valid distribution. In numerical applications, it would be bad if the limit throws an error even though the limit is a perfectly valid distribution. For example, you may have a model where λ = exp(x) and for very negative x this can underflow.