Probabilities.CauchyPDF Method

Overload List

#SignatureDescription
1procedure CauchyPDF(const X: TDenseMtxVec; m: Double; b: Double; const Res: TDenseMtxVec);Cauchy PDF (vectorized).
2function CauchyPDF(x: Double; m: Double; b: Double): Double;Cauchy probability density function (PDF).

Overload 1: procedure CauchyPDF(const X: TDenseMtxVec; m: Double; b: Double; const Res: TDenseMtxVec);

Cauchy PDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix.
2mLocation parameter, real value.
3bShape parameter, real positive value.
4ResAfter 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.

Result: stored in self (calling object)

Overload 2: function CauchyPDF(x: Double; m: Double; b: Double): Double;

Cauchy probability density function (PDF).

#NameDescription
1xFunction domain, real value.
2mLocation parameter, real value.
3bShape (scale) parameter, real positive value.

Returns: Double - 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