Definition: Joint cumulative distribution function

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Cumulative distribution function ▷ Joint cumulative distribution function

Definition: Let $X \in \mathbb{R}^{n \times 1}$ be an $n \times 1$ random vector. Then, the joint cumulative distribution function of $X$ is defined as the probability that each entry $X_i$ is smaller than a specific value $x_i$ for $i = 1, \ldots, n$:

\[\label{eq:cdf-joint} F_X(x) = \mathrm{Pr}(X_1 \leq x_1, \ldots, X_n \leq x_n) \; .\]

 

Sources:

• Wikipedia (2021): "Cumulative distribution function"; in: Wikipedia, the free encyclopedia, retrieved on 2021-04-07; URL: https://en.wikipedia.org/wiki/Cumulative_distribution_function#Definition_for_more_than_two_random_variables.

Metadata: ID: D141 | shortcut: cdf-joint | author: JoramSoch | date: 2020-04-07, 08:17.