Probabilities::JohnsonUBPDF Function

Overload List

#SignatureDescription
1double JohnsonUBPDF(double x, double gamma, double delta, double Lambda, double xi);Johnson unbounded (S_U) probability density function (PDF).
2void JohnsonUBPDF(TDenseMtxVec *X, double gamma, double delta, double Lambda, double xi, TDenseMtxVec *Res);Johnson unbounded (SU) distribution PDF (vectorized).

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

Johnson unbounded (S_U) probability density function (PDF).

#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) PDF for shape parameters gamma, delta, scale Lambda and location xi. Returns NaN if Lambda<=0 or delta<=0.

Remarks:

The Johnson S_U (unbounded) density. With z=(x-xi)/lambda and asinh(z)=ln(z+sqrt(1+z^2)),

PDF(x | gamma,delta,lambda,xi) = delta/(lambdasqrt(2pi)sqrt(1+z^2)) exp[-1/2(gamma+deltaln[z+sqrt(1+z^2)])^2] , z=(x-xi)/lambda .

Equivalent to scipy.stats johnsonsu(a=gamma, b=delta, loc=xi, scale=Lambda). Returns NaN for Lambda<=0 or delta<=0.

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

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

Johnson unbounded (SU) distribution PDF (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 PDF 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