Cumulative Distribution Function

The cumulative distribution function (CDF) is the probability that the variate takes on a value less than or equal to x:

For discrete distributions, this is expressed as

In this case, the empirical CDF is displayed as vertical lines at each integer x, and the theoretical PDF is displayed as a polygonal line:

For continuous distributions, the CDF is expressed as

,

so the theoretical CDF is displayed as a continuous curve. The empirical CDF is denoted by

,

and is displayed as a stepped discontinuous line depending on the number of bins:

See also:

• Creating Graphs