Add Distribution Fitting & Simulation Features to Your Applications
Domain Bounds
This section describes how the domain bounds affect the distribution fitting process (this applies to the continuous distributions only).
The SPAApplication.FitOptions.LBoundType and SPAApplication.FitOptions.UBoundType properties can take on the following values:
property value |
||
| SPABoundType.SPABoundUnknown | No information on distribution bounds available | |
| SPABoundType.SPABoundOpen | The distribution does not have a finite bound | |
| 3 | SPABoundType.SPABoundClosedEstimate | The distribution does have a finite bound, and this bound should be estimated from data |
| 4 | SPABoundType.SPABoundClosedFixed | The distribution has a finite bound (the exact bound values can be specified using the SPAApplication.FitOptions.LBoundValue and SPAApplication.FitOptions.UBoundValue properties) |
When you run the automated fit, the SPA SDK determines which distributions should be fitted. For example, if you set LBoundType to SPABoundClosedEstimate and UBoundType to SPABoundClosedEstimate, the SDK will only fit the non-negative and advanced distributions. Therefore, these settings combined define the applicable distribution types:
Fitting Non-Negative Distributions
The lower bound setting is applied when a non-negative distribution is fitted. The full form of the non-negative distributions will be fitted if you set LBoundType to SPABoundClosedEstimate. For example, the 3-parameter Weibull will be fitted and displayed on graphs as "Weibull (3P)", indicating the distribution name and the number of estimated parameters.
If you set the lower bound to a fixed value (LBoundType=SPABoundClosedFixed),
the location parameter 
will be assigned the value
of the LBoundValue property, and the rest of parameters will be estimated.
The fixed lower bound must not be greater than the minimum data value, otherwise the distribution will not be successfully fitted.
To fit the simplified form of the non-negative distributions, the lower bound should be set to a fixed value of zero. For example, the 2-parameter Weibull distribution will be fitted and displayed on graphs as "Weibull".
If you set LBoundType to SPABoundUnknown and run the fit, the SDK will fit both forms of the non-negative distributions. For example, both 2-parameter Weibull and 3-parameter Weibull distributions will be fitted.
Fitting Bounded Distributions
Both the lower bound and the upper bound settings are applied when a bounded distribution (except Johnson SB and Uniform) is fitted. For example, if you set both LBoundType and UBoundType to SPABoundClosedFixed, the lower boundary parameter and the upper boundary parameter will be assigned the values you specify. In this case, the boundary parameters will not be estimated: the SDK will estimate the rest of parameters only.
The fixed lower bound must not be greater than the minimum data value, and the fixed upper bound must not be less than the maximum data value.
On the other hand, you may want to fix one of these two bounds only, or even none of them. For example, if you want to fit the Beta distribution and set both bounds to SPABoundClosedEstimate (or SPABoundUnknown), all the four parameters of this distribution will be estimated.
Domain Bounds in Manual Fitting Mode
When you manually fit the distributions, a similar fitting algorithm is used. However, the default domain bounds do not affect the results: in this case, the SDK uses the specific distribution settings. For example, if the location parameter of the Gamma distribution is fixed, the SDK will only estimate the shape and the scale parameters.
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