Empirical Distribution
Formula and examples for the empirical distribution of a data series
In statistics, the empirical distribution function is a function which describes the proportion of values that are less than or equal to the comparison value. The result is between 0 and 1 inclusive.
Definition of the empirical distribution function
\(\displaystyle F_n(t)=\frac{Number \ of \ elements ≤ t}{n} \ \ = \frac{1}{n}\sum_{i-1}^{n} 1_{x_i} ≤t \)
Example
This example searches for the distribution for the following number series with 10 numbers
\(\displaystyle 2, 5, 4, 8, 3, 7, 9, 3, 1, 6 \)
5 is assumed as the comparison value. So the numbers are searched whose value is 5 or smaller.
\(\displaystyle \color{#44F}{2, 5, 4}, 8, \color{#44F}{3}, 7, 9, \color{#44F}{3, 1}, 6 \)
Of the 10 numbers, this applies to 6 numbers.
The empirical distribution is \(\displaystyle \frac{6}{10}= 0.6 \) oder \(60\%\)
Calculate empirical distribution online →
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