User`s guide

3 Fitting Data

3-20

difference is that the sum of sines equation includes the phase constant, and

does not include a DC offset term.

Weibull Distribution

The Weibull distribution is widely used in reliability and life (failure rate) data

analysis. The toolbox provides the two-parameter Weibull distribution

where a is the scale parameter and b is the shape parameter. Note that there

is also a three-parameter Weibull distribution with x replaced by x – c where c

is the location parameter. Additionally, there is a one-parameter Weibull

distribution where the shape parameter is fixed and only the scale parameter

is fitted. To use these distributions, you must create a custom equation.

Note that the Curve Fitting Toolbox does not fit Weibull probability

distributions to a sample of data. Instead, it fits curves to response and

predictor data such that the curve has the same shape as a Weibull

distribution.

Custom Equations

If the toolbox library does not contain the desired parametric equation, you

must create your own custom equation. However, if possible, you should use

the library equations because they offer the best chance for rapid convergence.

This is because

• For most models, optimal default coefficient starting points are calculated.

For custom equations, the default starting points are chosen at random on

the interval [0,1]. Refer to “Default Coefficient Parameters” on page 3-26 for

more information.

• An analytic Jacobian is used instead of finite differencing.

• When using the Analysis GUI, analytic derivatives are calculated as well as

analytic integrals if the integral can be expressed in closed form.

Note To save custom equations for later use, you should save the

curve-fitting session with the File-> Save Session menu item.

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b 1–

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