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WeibullDistribution

WeibullDistribution[Alpha, Beta]
represents a Weibull distribution with shape parameter Alpha and scale parameter Beta.
  • The probability density for value x in a Weibull distribution is proportional to x^(alpha-1)ⅇ^(-(x/beta)^alpha) for x>0, and is zero for x<0. »
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Basic Examples   (2)
The mean and variance of a Weibull distribution depend on the Gamma function:
Probability density function:
The mean and variance of a Weibull distribution depend on the Gamma function:
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Probability density function:
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Scope   (3)
Generate a set of pseudorandom numbers that are Weibull-distributed:
Properties based on higher order moments:
The q^(th) quantile of a Weibull distribution:
Applications   (3)
Plot the cumulative distribution function of a Weibull distribution:
A contour plot as both x and Alpha are varied:
A site has mean wind speed 7m/s and Weibull distribution with shape parameter 2:
The resulting wind speed distribution over a whole is then given by:
The power curve for a GE 1.5 MW wind turbine:
The total mean energy produced over the course of a year is then 4.3 MWh:
Properties & Relations   (4)
The probability density function integrates to unity:
WeibullDistribution is exponentially related to ExtremeValueDistribution:
WeibullDistribution is exponentially related to GumbelDistribution:
WeibullDistribution is related to ExponentialDistribution through a power:
Possible Issues   (3)
WeibullDistribution is not defined when either Alpha or Beta is not a positive real number:
The characteristic function of the Weibull distribution does not have a closed-form representation:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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