Definition:Cumulative Distribution Function

Definition
Let $\struct {\Omega, \Sigma, \Pr}$ be a probability space.

Let $X$ be a random variable on $\struct {\Omega, \Sigma, \Pr}$.

The cumulative distribution function (or c.d.f.) of $X$ is denoted $\map F X$, and defined as:
 * $\forall x \in \R: \map {\map F X} x := \map \Pr {X \le x}$

Also known as
Some sources refer to this as a distribution function, but it can then become confused with the concept of a in physics.

Others use the term probability distribution.

Some sources use the notation $\map \Phi X$ for $\map F X$.

Also see

 * Survival Function, a closely related concept


 * Properties of Cumulative Distribution Function