Empirical distribution function

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the <a href="/facts/Cumulative_distribution_function/WaKU8tp4">distribution function</a> associated with the <a href="/facts/Empirical_measure/cVHxwALN">empirical measure</a> of a <a href="/facts/Sampling_(statistics)/kIb01xdL">sample</a>. This <a href="/facts/Cumulative_distribution_function/WaKU8tp4">cumulative distribution function</a> is a <a href="/facts/Step_function/VnrEjo4B">step function</a> that jumps up by 1/n at each of the n data points. Its value at any specified value of the measured variable is the fraction of observations of the measured variable that are less than or equal to the specified value.
The empirical distribution function is an <a href="/facts/Estimator/CbkjcKvN">estimate</a> of the cumulative distribution function that generated the points in the sample. It converges with probability 1 to that underlying distribution, according to the <a href="/facts/Glivenko%E2%80%93Cantelli_theorem/o5E7Tjda">Glivenko–Cantelli theorem</a>. A number of results exist to quantify the rate of <a href="/facts/Convergence_of_random_variables/pWdatFlY">convergence</a> of the empirical distribution function to the underlying cumulative distribution function.

Empirical distribution function open-in-new

Empirical distribution function