Inverse Weibull Distribution

The inverse Weibull distribution, also known as the Fréchet distribution, is a special case of the generalized extreme value distribution.

The inverse Weibull distribution has a location parameter m (lower bound), a scale parameter s, and one shape parameter α which must be positive. The cumulative distribution function (CDF) has a relatively simple form:

$$F(x) = e^{-\left(\frac{x-m}{s}\right)^{-\alpha}}$$

The inverse Weibull distribution is implemented by the InverseWeibullDistribution class. It has two constructors.

The first constructor takes from one to three parameters. The first parameter is the shape parameter of the distribution. It must be greater than zero. The second is the scale parameter, which is optional with a default value of 1. The third is the location parameter, which is also optional with a default value of 0.

C# 
var invWeibull1 = new InverseWeibullDistribution(1.0);
var invWeibull2 = new InverseWeibullDistribution(1.0, 2.0);
var invWeibull3 = new InverseWeibullDistribution(1.0, 2.0, 3.0);

The second constructor is used to estimate the distribution from a sample. The first parameter is a Vector<T> that specifies the sample. The second parameter, which is optional, specifies the estimation method. This can be matching moments (the default) or maximum likelihood. Note that when estimating the distribution, the location parameter is always assumed to be zero.

C# 
var invWeibull4 = new InverseWeibullDistribution(new double[] 
    { 1.0, 2.0, 2.5, 4.0 });

The InverseWeibullDistribution class has three properties that return the LocationParameter, ScaleParameter, and ShapeParameter, respectively.

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..

See Also