English

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 ρ=pm1\rho=pm1, by Dirac's δ\delta-function. We also show how this representation allows to define Dirac's δ\delta-function as the ratio between bivariate distributions and the marginal distribution in the limit ρ±1\rho\rightarrow \pm1, 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}
}
R2 v1 2026-06-21T20:58:38.878Z