Johnson Bounded distribution



Format: JohnsonB(a1, a2, min, max)

The Johnson Bounded distribution has a range defined by the min and max parameters. Combined with its flexibility in shape, this makes it a viable alternative to the PERT, Triangle and Uniform distributions for modeling expert opinion. A public domain software product called VISIFIT allows the user to define the bounds and pretty much any two statistics for the distribution (mode, mean, standard deviation) and will return the corresponding distribution parameters.

Setting min to 0 and max to 1 gives a random variable that is sometimes used to model ratios, probabilities, etc. instead of a Beta or Kuramaswamy distribution.

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 Bounded distribution

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

VoseJohnsonBObject constructs a distribution object for this distribution.

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

VoseJohnsonBProb10 returns the log10 of the probability density or cumulative distribution function. 

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

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

VoseJohnsonBFitP returns the parameters of this distribution fitted to data.

 

Johnson Bounded distribution equations

 

 

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