More discrete distributions.

[JonasMoss]

Implement, possibly, the following discrete distributions:

Implement distributions

stats

These are extremely common.

• Binomial.
  • The ML doesn't always exist, since the Poisson is a limiting case.
• Negative binomial.
  • We have problems described here https://core.ac.uk/download/pdf/215229665.pdf with the Poisson limiting case being a problem. I think the estimator is OK now, but it may need more testing.
• Geometric.
• Poisson.

The hypegeometric distribution is common, but rarely used in the context of maximum likelihood estimation. Maximum likelihood would involve some sort of discrete optimization, and it will converge to binomial / Poisson for some data.

• Hypergeometric.

extraDistr

These are quite common and natural extensions of the distributions above. There are implementations of some of these already in e.g., iZID. But I'm not sure they are of sufficient quality as they use optimize, and may not estimate size in any case.

• Zero-inflated Possion.
• Beta-binomial. This one has several edge cases were the ML does not exist, and may be harder to implement. Analysis would, perhaps, warrant its own publication.
• Beta negative binomial.
• Zero-inflated negative binomial.

Other

• Zipf. (sads:dzipf as VGAM::dzipf is inaccurate.)
• Logarithmic series distribution (extraDistr::lgser). Uses the Lambert W function, which is good, since we've already used it in the zero-inflated Poisson.)
• Zeta distribution. Easy to implement. However, the VGAM implementation might be unreliable.
• Yule-Simon. It's easy to implement. But in VGAM.
• Conway--Maxwell Poisson. This one is by far the hardest, since it requires computation of a normalizing constant that has to my knowledge no excellent implementation.
• Conway--Maxwell binomial. Easier to compute since there is no infinite sum, but has Conway--Maxwell Poisson as a limiting case!

Add tests to implemented distributions.

• Binomial
• Negative binomial
• Zero-inflated Possion
• Geometric
• Poisson
• Zipf
• Logarithmic series distribution