On generalized binomial and multinomial distributions and their relation to generalized Poisson distributions

Binomial and multinomial distributions

Testing Poisson Binomial Distributions

A Poisson Binomial distribution over n variables is the distribution of the sum of n independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution P supported on {0, . . . , n} to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions. The sample complexity of our algorithm is O(n) to which we provid...

Asymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.

Characterizations of Certain Marshall-Olkin Generalized Distributions

Several characterizations of Marshall-Olkin generalized distributions, introduced by Gui (2013) and by Al-Saiari et al. (2014) are presented. These characterizations are based on: (i) a simple relationship between two truncated moments ; (ii) the hazard function.

Binomial and Poisson distributions as maximum entropy distributions

The binomial and the Poisson distributions are shown to be maximum entropy distributions of suitably defined sets. Poisson’s law is considered as a case of entropy maximization, and also convergence in information divergence is established.