Applies to: @RISK 5.x and Up

How @RISK calculates root-mean-square (RMS) error used to rank fitted

distributions

 

Explanation
For (x, p) data, @RISK compares the observed cumulative probabilities with those predicted by a candidate distribution. The RMS error is calculated as the square root of the mean of the squared differences between observed and predicted values:

RMS error = √[Σ(observed p – predicted p)² / n]

• Each data point contributes equally to the sum.

• Lower RMS error indicates a closer fit to the observed data.

• The calculation applies whether p represents cumulative probabilities or the area under a probability density curve.

Use in Fit Ranking
@RISK uses this RMS error to rank candidate distributions—the smaller the RMS error, the better the fit. This provides an objective measure to compare distributions.

Example
An attached workbook illustrates how @RISK computes RMS error using actual (x, p) data, showing step by step how observed cumulative probabilities are compared to predicted values from fitted distributions.

 

Related Article:

RMS Error Calculation in Distribution Fitting with (x,y) Pairs

Attachments:
RMSError_Example.xls