Probabilities.MaxwellCDF Method

Overload List

#SignatureDescription
1procedure MaxwellCDF(const X: TDenseMtxVec; a: Double; const Res: TDenseMtxVec);Maxwell CDF (vectorized).
2function MaxwellCDF(x: Double; a: Double): Double;Maxwell cumulative distribution function (CDF).

Overload 1: procedure MaxwellCDF(const X: TDenseMtxVec; a: Double; const Res: TDenseMtxVec);

Maxwell CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix with positive real values or zeros.
2aDistribution parameter, positive real value.
3ResAfter calculation stores the CDF calculated from X and a. 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 MaxwellCDF(x: Double; a: Double): Double;

Maxwell cumulative distribution function (CDF).

#NameDescription
1xFunction domain, zero or positive real value.
2aDistribution parameter, positive real value.

Returns: Double - the Maxwell cumulative distribution function (CDF) for value x using the parameter a. a must be positive and x >= 0, otherwise the result is NAN.

Remarks:

The Maxwell cumulative distribution function (standard, scale a) is

CDF(x| a)=erf(x/(sqrt(2) a))-sqrt(2/pi) x/aexp(-x^2/2a^2), x >= 0

equivalently 2 gamma(3/2, x^2/(2a^2)) / sqrt(pi) with the lower incomplete gamma function. It is the probability that a single observation falls in [0, x]. Domain: x >= 0 and a > 0; the result rises monotonically from 0 to 1. For a <= 0 or x < 0 the result is NAN.

See Also: Probabilities.MaxwellPDF, Probabilities.MaxwellCDFInv