Probabilities.CauchyCDFInv Method

Overload List

#SignatureDescription
1procedure CauchyCDFInv(const P: TDenseMtxVec; m: Double; b: Double; const Res: TDenseMtxVec);Cauchy PPF (vectorized).
2function CauchyCDFInv(p: Double; m: Double; b: Double): Double;Cauchy distribution point percent function (PPF).

Overload 1: procedure CauchyCDFInv(const P: TDenseMtxVec; m: Double; b: Double; const Res: TDenseMtxVec);

Cauchy PPF (vectorized).

#NameDescription
1PDefines distribution probabilities, real vector or matrix with values within closed interval [0,1].
2mLocation parameter, real value.
3bShape parameter, real positive value.
4ResAfter calculation stores the PPF calculated from P, 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 CauchyCDFInv(p: Double; m: Double; b: Double): Double;

Cauchy distribution point percent function (PPF).

#NameDescription
1pProbability, real value on closed interval [0,1].
2mLocation parameter, real value.
3bShape (scale) parameter, real positive value.

Returns: Double - the Cauchy distribution point percent function (PPF) for given parameters b and m. For p outside [0,1] or b <= 0 the result is NAN.

Remarks:

The inverse Cauchy cumulative distribution function (quantile) is

CDF^(-1)(p| m,b)=m+b tan[(p-1/2)pi]

It is the solution x of CDF(x | m,b) = p. Domain: probability p in [0,1], m any real value, scale b > 0. The tails diverge: as p -> 0 the result tends to minus infinity and as p -> 1 to plus infinity. For p < 0, p > 1, or b <= 0 the result is NAN.

See Also: Probabilities.CauchyPDF, Probabilities.CauchyCDF