Probabilities::JohnsonSBCDFInv Function

Probabilities Namespace

Overload List

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

Overload 1: double JohnsonSBCDFInv(double p, double gamma, double delta, double Lambda, double xi);

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

#NameTypeDescription
1pdoubleProbability, real value on the closed interval [0,1].
2gammadoubleDistribution shape parameter, real value.
3deltadoubleDistribution shape parameter, real positive value (delta>0).
4LambdadoubleDistribution scale parameter, real positive value (Lambda>0).
5xidoubleDistribution location parameter, real value.

Returns: 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
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler

Overload 2: void JohnsonSBCDFInv(TDenseMtxVec *P, double gamma, double delta, double Lambda, double xi, TDenseMtxVec *Res);

Johnson bounded (SB) distribution PPF (vectorized).

#NameTypeDescription
1PTDenseMtxVec *Defines distribution probabilities, real vector or matrix with values within closed interval [0,1].
2gammadoubleDistribution shape parameter, real value.
3deltadoubleDistribution shape parameter, real positive value.
4LambdadoubleDistribution scale parameter, real positive value.
5xidoubleDistribution location parameter, real value.
6ResTDenseMtxVec *After 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.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler