Probabilities::CauchyPDF Function

Overload List

#SignatureDescription
1double CauchyPDF(double x, double m, double b);Cauchy probability density function (PDF).
2void CauchyPDF(TDenseMtxVec *X, double m, double b, TDenseMtxVec *Res);Cauchy PDF (vectorized).

Overload 1: double CauchyPDF(double x, double m, double b);

Cauchy probability density function (PDF).

#NameTypeDescription
1xdoubleFunction domain, real value.
2mdoubleLocation parameter, real value.
3bdoubleShape (scale) parameter, real positive value.

Returns: the Cauchy probability density function (PDF) for given parameters b and m. Parameter b must be greater than zero, otherwise the result is NAN.

Remarks:

Calculates the Cauchy (Lorentz) probability density function

PDF(x| m,b)=1/pi*b/((x-m)^2+b^2)

where m is the location parameter (the peak of the distribution) and b is the scale parameter, equal to the half-width at half-maximum (HWHM). Domain: x is any real value; the location m is any real value and the scale b must be strictly positive. For b <= 0 the result is NAN. The Cauchy distribution has no defined mean or higher moments.

See Also: Probabilities::CauchyCDF, Probabilities::CauchyCDFInv
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void CauchyPDF(TDenseMtxVec *X, double m, double b, TDenseMtxVec *Res);

Cauchy PDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix.
2mdoubleLocation parameter, real value.
3bdoubleShape parameter, real positive value.
4ResTDenseMtxVec *After calculation stores the PDF calculated from X, m and b. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler