Aug 05

Univariate versus multivariate (Quant: Stat)

by David Harper, CFA, FRM, CIPM

FRM |

Learning objective: Distinguish between univariate and multivariate probability density functions

A single variable (univariate) probability distribution is concerned with only a single random variable; e.g., roll of a die, default of a single obligor. A multivariate probability density function concerns the outcome of an experiment with more than one random variable. This includes, the simplest case, two variables which is referred to as a bivariate distribution.

  Density Cumulative
Univariate f(x) = P(X = x) F(x) = P(X ≤ x)
Bivariate f(x) = P(X=x,Y=y) F(x) = P(X ≤ x, Y ≤ y)

Copula

A copula function nicely illustrates the difference between univariate and multivariate. The copula function takes as inputs univariate (marginal) unconditional probabilities and “joins” them to produce a multivariate distribution function:

copula

Comments

  1. Be the first to leave a comment!

Leave a Comment