Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure MaxwellPDF(const X: TDenseMtxVec; a: Double; const Res: TDenseMtxVec); | Maxwell PDF (vectorized). |
| 2 | function 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).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix with positive real values or zeros. |
| 2 | a | Distribution parameter, positive real value. |
| 3 | Res | After 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).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, zero or positive real value. |
| 2 | a | Distribution 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.
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.