The Weibull probability distribution, over the random variable x, has two parameters:

• k > 0, is the shape parameter
• λ > 0, is the scale parameter

Frequently engineers have data that is known to be well modeled by the Weibull distribution but the shape and scale parameters are unknown. In this case a data fitting strategy can be used; NMath now has a maximum likelihood Weibull fitting function demonstrated in the code example below.

    public void WiebullFit()
    {
      double[] t = new double[] { 16, 34, 53, 75, 93, 120 };
      double initialShape = 2.2;
      double initialScale = 50.0;

      WeibullDistribution fittedDist = WeibullDistribution.Fit( t, initialScale, initialShape );

      // fittedDist.Shape parameter will equal 1.933
      // fittedDist.Scale parameter will equal 73.526
    }

If the Weibull fitting algorithm fails the returned distribution will be null. In this case improving the initial parameter guesses can help. The WeibullDistribution.Fit() function accepts either arrays, as seen above, or DoubleVectors.

The latest version of NMath, including this maximum likelihood Weibull fit function, is available on the CenterSpace NuGet gallery.

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