Simulation Statistical Results

See also: Presenting results introduction, Graphical descriptions of model outputs

ModelRisk and Tamara risk analysis software offers a number of statistical descriptions to help analyze and compare results. Many statistical descriptions appear in the ‘Stats’ view within the Results Viewer after a simulation run.

The user may also wish to see statistical values appear directly within the spreadsheet at the end of a ModelRisk simulation run. ModelRisk provides a wide range of functions to perform this task, listed below.


VoseSimMean – returns the mean.

VoseSimMin – returns the minimum generated value.

VoseSimMax – returns the maximum generated value.

VoseSimPercentile – returns a specified percentile, e.g. the value for which 90% of the simulation results fell below.

VoseSimProbability – returns the probability of falling below the specified target value.

VoseSimMSE – returns the standard error of the mean.


VoseSimStdev – returns the standard deviation.

VoseSimVariance – returns the variance.

VoseSimCofV – returns the coefficient of variation.

VoseSimMeanDeviation – returns the mean absolute deviation.

VoseSimSemiStdev – returns the semi-standard deviation for a specified target.

VoseSimSemiVariance – returns the semi-variance for a specified target.


VoseSkewness – returns the skewness.

VoseKurtosis – returns the kurtosis.


VoseSimMoments – an array function returning the mean, variance, skewness and kurtosis.

Tail conditional mean values

VoseSimCVaRp – returns the conditional value at risk at some cumulative probability.

VoseSimCVaRx – returns the conditional value at risk at some target value.


VoseSimCorrelation – returns the correlation coefficient between two selected variables.

VoseSimCorrelationMatrix – an array function returning the correlation matrix between selected variables.


Use of these functions

Each of these simulation results statistical functions requires that one specify the target cell or a formula. For example:


specifies the target cell A1 and  will therefore  return the mean (average) of the values generated in cell A1 during a simulation. Similarly:


specifies a formula and will therefore return the mean of the square root of all the values generated in Cell A1, and:


will return the mean of values generated by simulating a Gamma(2,3) and a Normal(5,2) and adding these simulated values together.

If you are running more than one simulation (see VoseSimTable and Simulation Settings), you should also use the optional ‘Simulation ID’ parameter to specify the simulation number for which the statistical results should be displayed. For example:


will return mean of the values generated in cell A1 during the second simulation.

Some functions require one or more additional parameters: VoseSimPercentile requires that one specify the cumulative probability (a value between 0 and 1), VoseSimSemStdev requires that one specify the threshold value and whether the statistic applies to values above or below this threshold, etc.

All of these functions return the message “No simulation results” prior to running a simulation. Nearly all functions will update during a simulation. For example, VoseSimMean will continuously update the calculation during a simulation run, which can be viewed by selecting to refresh Excel during simulation in the Simulation Settings dialog:

VoseSimPercentile, VoseSimProbabilit, VoseSimCVaRp and VoseSimCVaRx however cannot display results during simulation because they require the complete simulation data set for their calculation. During simulation they return the message “Calculating…”.



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