Linear Transformations & the Multivariate Generating Function
Combinatorics
2012-09-18 v1 Probability
Statistics Theory
Statistics Theory
Abstract
This note examines linear combinations of multi-indexed sequences and derives the multivariate generating function of such a linear combination in terms of the original sequence's m.g.f. Applications include finding distributions and moments of non-negative discrete random variables conditioned on non-negative linear combinations of the original variables. Examples include independent Poisson r.v.'s and a -variate multinomial distribution.
Cite
@article{arxiv.1209.3357,
title = {Linear Transformations & the Multivariate Generating Function},
author = {Michael C. Burkhart},
journal= {arXiv preprint arXiv:1209.3357},
year = {2012}
}