functionnormalizePLpdf
Normalize a piecewise linear density function given by a list of points
Extends from Function ((Weighted) geometric mean).
Information
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The output y is a normalized piecewise linear probability distribution function specified by a list of points {{x1,f(x1)}, {x2,f(x2}}, ... ,{xn, f(xn)}, where the support may be rescaled to the unit interval (rescaleQ = true) and the area under the curve is equal to one.
Notes
If the normalization constant is not greater than zero, the function will simply return the input, albeit with possibly rescaled first dimension.
Syntax
Functions.normalizePLpdf({{x1,y1},{x2,y2}, ...}); // rescaleQ = true
Functions.normalizePLpdf({{x1,y1},{x2,y2}, ...}, rescaleQ = false);
Examples
normalizePLpdf({{0,2},{5,2},{10,2}}); // {{0,1},{0.5,1},{1,1}}
normalizePLpdf({{0,0},{5,1},{10,0}}); // {{0,0},{0.5,2},{1,0}}
normalizePLpdf({{0,2},{5,2},{10,2}}, false); // {{0,0.1},{5,0.1},{10,0.1}}
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | x (from geometricMean) | Vector input | |
| Real | weights (from geometricMean) | ones(size(x, 1)) | Vector of weights |
| Real | plPDF | Piecewise linear probability density function, i.e., { p1, p2, ... } | |
| Boolean | rescaleQ | true | = true, if support is to be rescaled to the unit interval |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | y (from geometricMean) |
Revisions
- Introduced in v2.1.0.