q-Probability: I. Basic Discrete Distributions

q-Probability: I. Basic Discrete Distributions

q-analogs of classical formulae go back to Euler, q-binomial coefficients were defined by Gauss, and q-hypergeometric series were found by E. Heine in 1846. The q-analysis was developed by F. Jackson at the beginning of the 20th century, and the modern point of view subsumes most of the old developments into the subjects of Quantum Groups and Combinational Enumeration. The general philosophy of...

Factorization of Discrete Probability Distributions

to belong to the graphical model. This direction was emphasized, for example, by Pearl (1988) and Geiger We formulate necessary and sufficient conditions for and Pearl (1993). Lauritzen (1996, Chapter 3) coman arbitrary discrete probability distribution to facpared these approaches and herein we extend his retor according to an undirected graphical model, or sults. a log-linear model, or other ...

Quantization of Discrete Probability Distributions

We study the problem of quantization of discrete probability distributions, arising in universal coding, as well as other applications. We show, that in many situations this problem can be reduced to the covering problem for the unit simplex. Such setting yields precise asymptotic characterization in the high-rate regime. Our main contribution is a simple and asymptotically optimal algorithm fo...

Modelling Discrete Input Probability Distributions

Sometimes input probability distributions for stochastic models are not so simple that standard distributions suit. In this case, we model with weighted sums of standard distributions. These composed distributions may have many parameters which must be estimated. This is not easy with common estimation methods like maximum-likelihood. We use the genetic algorithm for that. The design of the com...

Probability Distributions: Discrete vs. Continuous