Johnson Unbounded distribution



Format: JohnsonU(a1, a2, b, g)

The main use of the Johnson Unbounded distribution is that it can be made to have any combination of skewness and kurtosis. Thus, it provides a flexible distribution to fit to data by matching these moments. That said, it is an infrequently used distribution in risk analysis.

The distribution name comes from Johnson (1949) who proposed a system for categorizing distributions, in much the same spirit that Pearson did. Johnson's idea was to translate distributions to be a function of a unit Normal distribution, one of the few distributions for which there were good tools available at the time to handle.

ModelRisk functions added to Microsoft Excel for the Johnson Unbounded distribution

VoseJohnsonU generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseJohnsonUObject constructs a distribution object for this distribution.

VoseJohnsonUProb returns the probability density or cumulative distribution function for this distribution.

VoseJohnsonUProb10 returns the log10 of the probability density or cumulative distribution function.

VoseJohnsonUFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseJohnsonUFitObject constructs a distribution object of this distribution fitted to data.

VoseJohnsonUFitP returns the parameters of this distribution fitted to data.

 

Johnson unbounded distribution equations

 

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