Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure JohnsonUBCDF(const X: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec); | Johnson unbounded (SU) distribution CDF (vectorized). |
| 2 | function JohnsonUBCDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double; | Johnson unbounded (S_U) cumulative distribution function (CDF). |
Overload 1: procedure JohnsonUBCDF(const X: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);
Johnson unbounded (SU) distribution CDF (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 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. |
Result: stored in self (calling object)
Overload 2: function JohnsonUBCDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;
Johnson unbounded (S_U) cumulative distribution function (CDF).
| # | 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) 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.