Relationship between cdf and density (histogram) plots

See also: Cumulative probability plots, Second order cumulative probability plot, Presenting results introduction, Graphical descriptions of model outputs, Histogram (density) plots

For a continuous variable the gradient of a cdf plot is equal to the probability density at that value. That means that the steeper the slope of a cdf the higher a relative frequency (histogram) plot would look at that point:

The disadvantage of a cdf is that one cannot readily determine the central location or shape of the distribution. We cannot easily recognize common distributions like a Triangle(2, 3,6), normal, and uniform. Looking at the plots below, you will readily identify the distribution form from the left panels, but not so easily from the right panels:

For a discrete distribution, the cdf increases in steps equal to the probability of the x-value occurring:

Read on: Ascending and descending cumulative plots



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