Inter-percentile range

See also: Statistical descriptions of model outputs, Variance, Inter-percentile range, Mean deviation (MD)

The inter-percentile range of an output is calculated as the difference between two percentiles, for example:

x95-x05 to give the central 90% range

x90 - minimum to give the lower 90% range

x90 - x10 to give the central 80% range

The inter-percentile range is a stable measure of spread (unless one of the percentiles is the minimum or maximum), meaning that the value is quickly obtained for relatively few iterations of a model. It also has the great advantage of having a consistent interpretation between distributions.

One potential problem you should be aware of is with applying an inter-percentile range calculation to a discrete distribution, particularly when there are only a few important values:

 

In this example, several key cumulative percentiles fall on the same values, so of course several different inter-percentile ranges take the same values. In addition, the inter-percentile range becomes very sensitive to the percentile chosen. In the plot above, for example:

x95 - x05 = 4 - 1 = 3, but

x96 - x04 = 5 - 0 = 5.

Read on: Variance

 

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