Definition:Cumulative Frequency/Relative

Definition

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

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

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

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

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Examples

Arbitrary Example

Consider the sample:

$2, 5, 3, 3, 3, 5, 3, 6, 2, 3, 9, 5$

There are $12$ observations in this sample.

The relative cumulative frequency of the observation $5$ is $\dfrac {10} {12} = \dfrac 5 6$.

Also see

• Results about cumulative distribution functions 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.