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Weibull(Location,Scale,Shape), usually Weibull(0,b,a)

Weibull equations

Crystal Ball parameter restrictions




Examples of the Weibull distribution are given below:




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. Example: Light bulbs.


The Weibull distribution becomes an exponential distribution when a = 1, i.e. Weibull(0,b,1) = Exponential(1/b). The Weibull distribution is very close to the Normal distribution when b = 3.25. The Weibull distribution is named after the Swedish physicist Dr E. H. Wallodi Weibull (1887-1979)  who used it to model the distribution of the breaking strengths of materials.


The Excel function WEIBULL(x,a,b,0) returns the probability density function for the Weibull(0,b,a) distribution, while WEIBULL(x,a,b,1) returns its cumulative distribution function.





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