Weibull distribution | Vose Software

Weibull distribution

Format: Weibull(a, b)



The Weibull distribution is often used to model the time until occurrence of an event where the probability of occurrence changes with time (the process has 'memory'), as opposed to the Exponential distribution where the probability of occurrence remains constant ('memoryless'). It has also been used to model variation in wind speed at a specific site.


The Weibull distribution becomes an exponential distribution when a = 1, i.e. Weibull(1, b) = Expon(b). The Weibull distribution is very close to the Normal distribution when b= 3.25.

The Weibull distribution is named after the Swedish physicist E. H. Waloddi Weibull who used it to model the distribution of the breaking strengths of materials, a use it still has today.

Alternative parameterizations

The WeibulAlt distribution determines a Weibull distribution defined by two percentiles.

ModelRisk functions added to Microsoft Excel for the Weibull distribution

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

VoseWeibullObject constructs a distribution object for this distribution.

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

VoseWeibullProb10 returns the log10 of the probability density or cumulative distribution function. 

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

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

VoseWeibullFitP returns the parameters of this distribution fitted to data.


Weibull distribution equations