We investigate the class of splitting distributions as composition a singular multivariate distribution and univariate distribution. It will be shown that most common parametric count (multinomial, negative multinomial, hypergeometric, …) can written with separate parameters for both components, thus facilitating their interpretation, inference, study probabilistic characteristics extensions to...

Stylometry refers to the statistical analysis of literary style of authors based on the characteristics of expression in their writings. We propose an approach to stylometry based on a Bayesian Dirichlet process mixture model using multinomial word frequency data. The parameters of the multinomial distribution of word frequency data are the “word prints” of the author. Our approach is based on ...

Abstract In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter,...

This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur natural...

A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimat...

The Dirichlet compound multinomial (DCM) distribution has recently been shown to be a good model for documents because it captures the phenomenon of word burstiness, unlike standard models such as the multinomial distribution. This paper investigates the DCM Fisher kernel, a function for comparing documents derived from the DCM. We show that the DCM Fisher kernel has components that are similar...

We explore a number of problems related to learning and covering structured distributions. Hypothesis Selection: We provide an improved and generalized algorithm for selecting a good candidate distribution from among competing hypotheses. Namely, given a collection of N hypotheses containing at least one candidate that is ε-close to an unknown distribution, our algorithm outputs a candidate whi...