Weibull distribution with alternative parameters



Format: WeibullAlt(Value1, Prob1, Value2, Prob2, Minimum)

Uses

This alternative parameterization of the Weibull distribution is useful for modeling expert estimates of some continuous quantity with a long right tail, like time or cost to complete a task. It is often more easy for experts to talk about percentiles, like “there is a 5% chance the cost will be less than $100k”. This parameterization allows one to define a distribution using two percentiles and a minimum.

The WeibullAlt distribution appears in ModelRisk's standard Select Distribution palette. It also appears in the Expert selector window in ModelRisk when one selects two percentiles {(Value1, Prob1), (Value2, Prob2)} and a minimum.

ModelRisk has two other distributions that can be used with this alternative parametization: the LognormalAlt and the LogLogisticAlt. It is a good idea to compare all three distributions together to see which gives the most realistic interpretation of the input parameters.

ModelRisk functions added to Microsoft Excel for the Alternative-Parameter Weibull distribution

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

VoseWeibullAltObject constructs a distribution object for this distribution.

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

VoseWeibullAltProb10 returns the log10 of the probability density or cumulative distribution function.

 

Alternative-Parameter Weibull distribution equations

 

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