functionnormalizePLpdf

Normalize a piecewise linear density function given by a list of points

Extends from Function (Icon for functions).

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	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		Normalized distribution density function with support [0,1]

Revisions

Introduced in v2.1.0.