Probabilities.JohnsonSBCDFInv Method

Overload List

#SignatureDescription
1procedure JohnsonSBCDFInv(const P: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);Johnson bounded (SB) distribution PPF (vectorized).
2function JohnsonSBCDFInv(p: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;Johnson bounded (S_B) percent point function (PPF, quantile / inverse CDF).

Overload 1: procedure JohnsonSBCDFInv(const P: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);

Johnson bounded (SB) distribution PPF (vectorized).

#NameDescription
1PDefines distribution probabilities, real vector or matrix with values within closed interval [0,1].
2gammaDistribution shape parameter, real value.
3deltaDistribution shape parameter, real positive value.
4LambdaDistribution scale parameter, real positive value.
5xiDistribution location parameter, real value.
6ResAfter calculation stores the PPF calculated from P, gamma, delta, Lambda and xi. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of P.

Result: stored in self (calling object)

Overload 2: function JohnsonSBCDFInv(p: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;

Johnson bounded (S_B) percent point function (PPF, quantile / inverse CDF).

#NameDescription
1pProbability, real value on the closed interval [0,1].
2gammaDistribution shape parameter, real value.
3deltaDistribution shape parameter, real positive value (delta>0).
4LambdaDistribution scale parameter, real positive value (Lambda>0).
5xiDistribution location parameter, real value.

Returns: Double - the value x such that JohnsonSBCDF(x,gamma,delta,Lambda,xi)=p. Returns NaN if Lambda<=0, delta<=0, or p is outside [0,1].

Remarks:

Inverting the CDF, with Phi^(-1) the standard normal quantile and r=exp[(Phi^(-1)(p)-gamma)/delta],

CDFInv(p | gamma,delta,lambda,xi) = xi + lambda z , z = r/(r+1) , r = exp[(Phi^(-1)(p)-gamma)/delta] .

Returns NaN for Lambda<=0, delta<=0, or p outside [0,1].

See Also: Probabilities.JohnsonSBCDF, Probabilities.JohnsonSBPDF