> In addition, every person who ever wrote code in the future that worked > with Poisson objects would need to know that our definition of the Poisson > distribution contradicted the definition found in textbooks. >
but does it really? the pmf should be P(n) = lambda^n/n! exp[-lambda] . plugging in lambda = 0 gives P(n) = KroneckerDelta(n,0) since 0^0=1 . everything is fine. i agree that the support is different but that seems to be a numerical problem when calculating KL divergences, not a mathematical one.
