`PsiMean (cell,simulation)`

PsiMean returns the mean value for the specified uncertain function cell.  The mean or average value is the 1st moment of the distribution of trials and is computed as:

The mean is frequently used as a measure of central tendency or the “middle” of an uncertain function; but for skewed distributions, care must be taken in using the mean as a measure of central tendency because the mean is easily distorted by extreme outlier values.

Two additional arguments are utilized when a Psi Statistic function is used with Dimensional Modeling: Struc_format and Param_slice.

`PsiMean (cell,simulation,struc_format,param_slice)`

Struc_format: This argument is an optional argument entered as a string. If omitted, all cube values will be printed in a single column. If “dims” is passed for this argument, the Psi Statistic function will print all dimensions in the cube with their lengths so the user can be advised of the size of the cubes and will be able to estimate the range needed when entering the Psi Statistic function as an array formula. If “vals” is passed for this argument, the result values will be displayed along with the dimension elements in the form of a relational or pivot table. Please see the Simulation example in the Dimensional Modeling chapter in Frontline Solvers User Guide for more information on this function. It’s also possible to use this argument to return the name of a specific element in a cube containing one or more structural dimensions.

To use this argument to return the value of a specific element in a 1-dimensional cube (containing a structural dimension), use the form: “ [StructuralDimisension1].[Element1]”. To use this argument to return the value of a 2-dimensional cube (containing structural dimensions), use the form: “[StructuralDimension1].[Element],[StructuralDimension2].[Element]”.

To use this argument to return the value of a N-dimensional cube (containing structural dimensions), use the form: “[StructuralDimension1].[Element],[StructuralDimension2].[Element],…,[StructuralDimensionN].[Element]”.

Param_slice: The param_slice argument is an optional string argument specifying the desired element “slice” for the parametric dimensions. If omitted the elements selected in the pane will be used. It’s also possible to use this argument to return the value of a specific element in a cube containing one or more parametric dimensions.

To use this argument to return the value of a specific element in a 1-dimensional cube (containing a parametric dimension), use the form: “[ParametricDimisension1].[Element1]”.

To use this argument to return the value of a 2-dimensional cube (containing parametric dimensions), use the form: “[ParametricDimension1].[Element],[ParametricDimension2].[Element]”.

### Compound Distributions

Analytic Solver computes the mean of a compound distribution as:

Mean  = N * distr mean

Where N is the compound size and distr mean is the analytical mean of the underlined distribution.

For example, for the compound distribution, PsiNormal(m, std), N times, the mean of the compound distribution is N * m.