Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure JohnsonUBCDFInv(const P: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec); | Johnson unbounded (SU) distribution PPF (vectorized). |
| 2 | function JohnsonUBCDFInv(p: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double; | Johnson unbounded (S_U) percent point function (PPF, quantile / inverse CDF). |
Overload 1: procedure JohnsonUBCDFInv(const P: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);
Johnson unbounded (SU) distribution PPF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | P | Defines distribution probabilities, real vector or matrix with values within closed interval [0,1]. |
| 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 PPF calculated from P, gamma, delta, Lambda and xi. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of P. |
Result: stored in self (calling object)
Overload 2: function JohnsonUBCDFInv(p: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;
Johnson unbounded (S_U) percent point function (PPF, quantile / inverse CDF).
| # | Name | Description |
|---|---|---|
| 1 | p | Probability, real value on the closed interval [0,1]. |
| 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 value x such that JohnsonUBCDF(x,gamma,delta,Lambda,xi)=p. Returns NaN if Lambda<=0, delta<=0, or p is outside [0,1].
Remarks:
Inverting the CDF, with Phi^(-1) the standard normal quantile and r=exp[(Phi^(-1)(p)-gamma)/delta],
CDFInv(p | gamma,delta,lambda,xi) = xi + lambda z , z = sinh[(Phi^(-1)(p)-gamma)/delta] = 1/2(r-1/r) .
Returns NaN for Lambda<=0, delta<=0, or p outside [0,1].