Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void JohnsonUBPDF(TDenseMtxVec X, Double gamma, Double delta, Double Lambda, Double xi, TDenseMtxVec Res) | Johnson unbounded (SU) distribution PDF (vectorized). |
| 2 | Double 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).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, vector or matrix with real values. |
| 2 | gamma | Distribution shape parameter, real value. |
| 3 | delta | Distribution shape parameter, real positive value. |
| 4 | Lambda | Distribution scale parameter, real positive value. |
| 5 | xi | Distribution location parameter, real value. |
| 6 | Res | 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. |
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).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value (unbounded support, all real x). |
| 2 | gamma | Distribution shape parameter, real value. |
| 3 | delta | Distribution shape parameter, real positive value (delta>0). |
| 4 | Lambda | Distribution scale parameter, real positive value (Lambda>0). |
| 5 | xi | Distribution 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.