Probabilities::JohnsonUBCDF Function

Overload List

#SignatureDescription
1double JohnsonUBCDF(double x, double gamma, double delta, double Lambda, double xi);Johnson unbounded (S_U) cumulative distribution function (CDF).
2void JohnsonUBCDF(TDenseMtxVec *X, double gamma, double delta, double Lambda, double xi, TDenseMtxVec *Res);Johnson unbounded (SU) distribution CDF (vectorized).

Overload 1: double JohnsonUBCDF(double x, double gamma, double delta, double Lambda, double xi);

Johnson unbounded (S_U) cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, real value (unbounded support, all real x).
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 Johnson unbounded (S_U) CDF for shape parameters gamma, delta, scale Lambda and location xi. Returns NaN if Lambda<=0 or delta<=0.

Remarks:

With z=(x-xi)/lambda and Phi the standard normal CDF,

CDF(x | gamma,delta,lambda,xi) = Phi[gamma+deltaln(z+sqrt(1+z^2))] , z=(x-xi)/lambda .

Equivalent to scipy.stats johnsonsu(a=gamma, b=delta, loc=xi, scale=Lambda); monotone non-decreasing on all real x. Returns NaN for Lambda<=0 or delta<=0.

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

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

Johnson unbounded (SU) distribution CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, vector or matrix with real values.
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 CDF calculated from X, agmma, delta, Lambda and xi. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler