Probabilities.JohnsonUBPDF Method

Overload List

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

Overload 1: void JohnsonUBPDF(TDenseMtxVec X, Double gamma, Double delta, Double Lambda, Double xi, TDenseMtxVec Res)

Johnson unbounded (SU) distribution PDF (vectorized).

#NameDescription
1XDefines distribution domain, vector or matrix with real values.
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 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.

Result: stored in self (calling object)

Overload 2: Double JohnsonUBPDF(Double x, Double gamma, Double delta, Double Lambda, Double xi)

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

#NameDescription
1xFunction domain, real value (unbounded support, all real x).
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 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