Probabilities::JohnsonUBCDFInv Function

Overload List

#SignatureDescription
1double JohnsonUBCDFInv(double p, double gamma, double delta, double Lambda, double xi);Johnson unbounded (S_U) percent point function (PPF, quantile / inverse CDF).
2void JohnsonUBCDFInv(TDenseMtxVec *P, double gamma, double delta, double Lambda, double xi, TDenseMtxVec *Res);Johnson unbounded (SU) distribution PPF (vectorized).

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

Johnson unbounded (S_U) 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 JohnsonUBCDF(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 = sinh[(Phi^(-1)(p)-gamma)/delta] = 1/2(r-1/r) .

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

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

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

Johnson unbounded (SU) 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