Definition:Cumulative Frequency

Definition

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

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

Absolute

The absolute cumulative frequency of $X$ is defined as:

$\forall x \in \Dom X: \map {\text {acf} } x = \ds \sum_{y \mathop \le x} \map \Omega y$

Relative

The relative cumulative frequency of $X$ is defined as:

$\forall x \in \Dom X: \map {\text {acf} } x = \dfrac {\ds \sum_{y \mathop \le x} \map \Omega y} {\size {\Dom X} }$

Also see

• Results about cumulative frequency can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): frequency: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): frequency: 2.