HomeTechniques and Tips@RISK Distribution FittingBounds of Fitted Uniform and Exponential Distributions

4.13. Bounds of Fitted Uniform and Exponential Distributions

Applies to: @RISK 6.x/7.x, Professional and Industrial Editions

When I fit points to the continuous distributions RiskUniform and RiskExpon, the minimum of the fitted distribution is to the left of the smallest data value.  The maximum of the fitted RiskUniform is to the right of the largest data value.

This seems strange at first, but it actually makes good sense if you look deeper.  Here are two explanations:

This issue will come up in any bounded continuous distribution, where the probability density shifts abruptly at the left from zero to a positive value, or at the right from a positive value to zero.

For example, if you fit the points {11,12,13,14,15} as a continuous uniform distribution, you get RiskUniform(10,16), not RiskUniform(11,15) as you might expect at first. (Please see attached illustration.)  To make μmin and μmax equal the minimum and maximum of the sample data, @RISK applies a bias correction of (maxmin)/(n–1) = (15–11)/(5–1) = 1, so the minimum and maximum of the RiskUniform are 1 unit left and right of the minimum and maximum of the data.  For the points {11,11.5,12,12.5,13,13.5,14,14.5,15}, the bias correction is 0.5, and the fitted uniform function is RiskUniform(10.5,15.5).

For the exponential function, the bias correction is (meanmin)/n. Again considering the points {11,12,13,14,15}, the bias correction is (13–11)/5 = 0.4. (Please see attached illustration.)

Last edited: 2015-06-19

Downloads

This page was: Helpful | Not Helpful