Definition:Cumulative Frequency/Relative
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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.