Multinomial and Hypergeometric Distributions in Markov Categories

Binomial and multinomial distributions

On Dirichlet Multinomial Distributions

Dedicated to Professor Y. S. Chow on the Occasion of his 80th Birthday By Robert W. Keener and Wei Biao Wu Abstract Let Y have a symmetric Dirichlet multinomial distributions in R, and let Sm = h(Y1)+· · ·+h(Ym). We derive a central limit theorem for Sm as the sample size n and the number of cells m tend to infinity at the same rate. The rate of convergence is shown to be of order m. The approa...

Multinomial nonparametric predictive inference with sub - categories

Nonparametric predictive inference (NPI) is a powerful tool for predictive inference under nearly complete prior ignorance. After summarizing our NPI approach for multinomial data, as presented in [8, 9], both for situations with and without known total number of possible categories, we illustrate how this approach can be generalized to deal with sub-categories, enabling consistent inferences a...

Characterization of Subfamily in Gaussian Hypergeometric Distributions

A characterization theorem based on first moment is given for the subfamily of distributions generated by the Gaussian hypergeometric function. The theorem is then applied to some discrete probability distributions, providing specific characterization theorems for each of them.

Dagger categories and formal distributions

Monoidal dagger categories play a central role in the abstract quantum mechanics of Abramsky and Coecke. The authors show that a great deal of elementary quantum mechanics can be carried out in these categories; for example, the Born rule emerges naturally. In this paper, we construct a category of tame formal distributions with coefficients in a commutative associative algebra and show that it...