A note on the bivariate distribution representation of two perfectly correlated random variables by Dirac's $\delta$-function
Networking and Internet Architecture
2012-05-07 v1
Abstract
In this paper we discuss the representation of the joint probability density function of perfectly correlated continuous random variables, i.e., with correlation coefficients , by Dirac's -function. We also show how this representation allows to define Dirac's -function as the ratio between bivariate distributions and the marginal distribution in the limit , whenever this limit exists. We illustrate this with the example of the bivariate Rice distribution
Cite
@article{arxiv.1205.0933,
title = {A note on the bivariate distribution representation of two perfectly correlated random variables by Dirac's $\delta$-function},
author = {Andrés Alayón Glazunov and Jie Zhang},
journal= {arXiv preprint arXiv:1205.0933},
year = {2012}
}