Weibull parameter estimation

[norbert.bakkers@lr.org]

Is it possible to estimate the Weibull shape, scale and location parameters of a measured dataset using the Inductive Statistics Option?
If this is possible, what parameter estimation approach is used? (Rank regression on x or Y, maximum likelihood estimation,…)

[norbert.bakkers@lr.org]

Is it possible to estimate the Weibull shape, scale and location parameters of a measured dataset using the Inductive Statistics Option?
If this is possible, what parameter estimation approach is used? (Rank regression on x or Y, maximum likelihood estimation,…)

[Bernhard Kantz]

It’s not possible to estimate the parameters of a Weibull distribution using the Inductive Statistics option. With this option you can calculate the Weibull distribution or density function using the Distribution Analysis Object.

But you could use the Non-Linear Curve Fit Analysis Object to estimate the parameters. Here it’s possible to create your own user-defined function (Example: Weibul density function):

Dim a = p[0]
Dim b = p[1]
a * b *x^(b-1)*E^(-a*x^b)

With the analysis object you can estimate the parameters a and b.
The algorithm is is based on the Newton method of least squares.

Support@weisang.com

[norbert.bakkers@lr.org]

Could you please give a full example how I should implement this in a formula?
I assume the ‘Approximation’ tool should be used. The problem I have is that ‘Approximation’ only allows the selection of a number of set initial functions but does not allow me to use the exact weibull distribution. How should I continue?

[Bernhard Kantz]

You have to use the Non-Linear Curve Fitting Analysis Object instead of the Approximation function because the Weibull function is a non-linear function.
With the Non-Linear Curve Fitting analysis object, you can converge a model function dependent on an independent variable and several parameters toward a given data set. A number of pre-defined model functions are available to do this. Alternatively, you can define particular models.

E.g. you can use the predefined Weibull model (variante 1). Certain parameters of the selected model can be declared as fixed.

See also
Non-Linear Curve Fitting Analysis Object
Non-Linear Curve Fitting Tutorial
NonLinCurveFit function

support@weisang.com

[norbert.bakkers@lr.org]

I currently use Flexpro 6 with the count option. As I cannot find the nonlinear function, I assume either Flexpro 7 or another option is required. What do I need for the nonlinear function?

[Bernhard Kantz]

The non-linear curve fitting object is available in FlexPro 7. For this feature no additional option is necessary.

Support@weisang.com

[Author]

Posts