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Lambda Function Reference
Simulation
Fkmin

Fkmin

Description

The Fleishman power method is used to generate random numbers drawn from a population with a specified skewness and kurtosis. The lambda function that does this is rerror (or rerrorV), which is also used in MCM / MCM_V.

But when one specifies a skew, there is a minimum kurtosis that is also present. If the user requests a kurtosis lower than this value, an error results. This Fkmin function can be used to avoid that error when using rerror~/~rerrorV and MCM/MCM_V (which both use rerror).

Syntax

Fkmin(skew), where skew is the desired skew for a Fleishman RNG. The function returns the minimum kurtosis needed in Fleishman’s RNG transformation.

Example

Consider the example in the image below. The syntax for rerror is rerror(rows,cols,skew,kurt) so the formula below is requesting 100 random numbers as a column vector. The cell D3 contains the desired skew (1) and the cell D4 contains the requested kurtosis (0). But that kurtosis is not compatible with the requested skew and would return an error. Instead the cell formula uses L.Fkmin(D3) as a fallback value to request the minimum possible kurtosis that is consistent with the requested skew. If the user enters a value higher than that minimum in cell D4 then it will be used.

rerror called with skew 1 and kurtosis 0, using MAX(Fkmin(skew), kurtosis) so the kurtosis is never below the minimum allowed

Source Code 

Fkmin = LAMBDA(
    skew,
    -1.13168 + 1.58837*skew^2
);
GetSeedMCM(_V)