Probabilities.JohnsonSBCDF Method

Overload List

#SignatureDescription
1procedure JohnsonSBCDF(const X: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);Johnson bounded (SB) distribution CDF (vectorized).
2function JohnsonSBCDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;Johnson bounded (S_B) cumulative distribution function (CDF).

Overload 1: procedure JohnsonSBCDF(const X: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);

Johnson bounded (SB) distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, vector or matrix with real values on closed interval [xi,xi+Lambda].
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 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 JohnsonSBCDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;

Johnson bounded (S_B) cumulative distribution function (CDF).

#NameDescription
1xFunction domain, real value on the closed interval [xi, xi+Lambda].
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 bounded (S_B) CDF for shape parameters gamma, delta, scale Lambda and location xi. Returns NaN if Lambda<=0, delta<=0, or x outside [xi, xi+Lambda].

Remarks:

With z=(x-xi)/lambda in (0,1) and Phi the standard normal CDF,

CDF(x | gamma,delta,lambda,xi) = Phi[gamma+deltaln(z/(1-z))] , z=(x-xi)/lambda .

Equivalent to scipy.stats johnsonsb(a=gamma, b=delta, loc=xi, scale=Lambda); monotone non-decreasing on [xi, xi+Lambda]. Returns NaN for Lambda<=0, delta<=0, or x outside the support.

See Also: Probabilities.JohnsonSBPDF, Probabilities.JohnsonSBCDFInv