Probabilities.JohnsonSBPDF Method

Overload List

#SignatureDescription
1procedure JohnsonSBPDF(const X: TDenseMtxVec; gamma: Double; delta: Double; Lambda: Double; xi: Double; const Res: TDenseMtxVec);Johnson bounded (SB) distribution PDF (vectorized).
2function JohnsonSBPDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;Johnson bounded (S_B) probability density function (PDF).

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

Johnson bounded (SB) distribution PDF (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 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: function JohnsonSBPDF(x: Double; gamma: Double; delta: Double; Lambda: Double; xi: Double): Double;

Johnson bounded (S_B) probability density function (PDF).

#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) PDF for shape parameters gamma, delta, scale Lambda and location xi. Returns NaN if Lambda<=0, delta<=0, or x outside [xi, xi+Lambda].

Remarks:

The Johnson S_B (bounded) density. With z=(x-xi)/lambda in (0,1),

PDF(x | gamma,delta,lambda,xi) = delta/(lambdasqrt(2pi) z(1-z)) exp[-1/2(gamma+deltaln[z/(1-z)])^2] , z=(x-xi)/lambda .

Equivalent to scipy.stats johnsonsb(a=gamma, b=delta, loc=xi, scale=Lambda). Returns NaN for Lambda<=0, delta<=0, or x outside [xi, xi+Lambda].

See Also: Probabilities.JohnsonSBCDF, Probabilities.JohnsonSBCDFInv