Probabilities.MaxwellPDF Method

Overload List

#SignatureDescription
1procedure MaxwellPDF(const X: TDenseMtxVec; a: Double; const Res: TDenseMtxVec);Maxwell PDF (vectorized).
2function MaxwellPDF(x: Double; a: Double): Double;Maxwell probability density function (PDF).

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

Maxwell PDF (vectorized).

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

Maxwell probability density function (PDF).

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

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

Remarks:

The routine evaluates, for x >= 0,

PDF(x| a)=sqrt(2/(pi a)) x^2/a^2exp(-x^2/2a^2)

Note: this expression carries an extra factor of sqrt(a) relative to the standard normalized Maxwell density (which is sqrt(2/pi) x^2/a^3 exp(-x^2/2a^2)); consequently it integrates to sqrt(a) rather than 1 and is not the exact derivative of MaxwellCDF (which IS the standard normalized CDF with scale a). The relation MaxwellPDF(x,a) = sqrt(a) * d/dx MaxwellCDF(x,a) holds. Domain: x >= 0 and a > 0. For a <= 0 or x < 0 the result is NAN.

See Also: Probabilities.MaxwellCDF, Probabilities.MaxwellCDFInv