The Weibull Distribution

The Weibull distribution can be used to model the lifetime of equipment in reliability engineering.

The Weibull distribution has a scale parameter and a shape parameter often called the order. These parameters are usually denoted by the Greek letters β and η. η is the scale parameter, and is often called the characteristic life. β is a shape parameter.

The probability density function is:

The Weibull distribution may also have a location parameter, which translates the distribution functions up or down the X axis by the specified amount.

The Weibull distribution is implemented by the WeibullDistribution class. It has one constructor with two arguments. The first argument is the location parameter, and corresponds to the mode of the probability density function. The second argument is the scale parameter.

The following constructs the same Weibull distribution with scale parameter 6.8 and shape parameter 4.1:

var weibull = new WeibullDistribution(6.8, 4.1);

Dim weibull = New WeibullDistribution(6.8, 4.1)

let weibull = WeibullDistribution(6.8, 4.1)

The WeibullDistribution class has three specific properties, LocationParameter, ScaleParameter and ShapeParameter, which return the parameters of the distribution.

WeibullDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator. The second and third parameters are the location and scale parameters of the distribution.

var random = new MersenneTwister();
double sample = WeibullDistribution.Sample(random, 6.8, 4.1);

Dim random = New MersenneTwister()
Dim sample = WeibullDistribution.Sample(random, 6.8, 4.1)

let random = MersenneTwister()
let sample = WeibullDistribution.Sample(random, 6.8, 4.1)

The above example uses the MersenneTwister class to generate uniform random numbers.

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