Evaluates the F probability density function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double F(
	double x,
	double dfn,
	double dfd
)
Visual Basic (Declaration)
Public Shared Function F ( _
	x As Double, _
	dfn As Double, _
	dfd As Double _
) As Double
Visual C++
public:
static double F(
	double x, 
	double dfn, 
	double dfd
)

Parameters

x
Type: System..::.Double
A double, the argument at which the function is to be evaluated.
dfn
Type: System..::.Double
A double, the numerator degrees of freedom. It must be positive.
dfd
Type: System..::.Double
A double, the denominator degrees of freedom. It must be positive.

Return Value

A double, the value of the probability density function at x.

Remarks

The probability density function of the F distribution is

{\it f}(x, {\it dfn}, {\it dfd})= {\frac { {\Gamma}(\frac {v_1 + v_2}{2})({\frac {v_1}{v_2})}^{\frac{v_1}{2}} x^{\frac {v_1}{2}} } {{{\Gamma}(\frac {v_1}{2}) }{{\Gamma}(\frac {v_2}{2}) } {(1+\frac{v_1x}{v_2})}^{\frac{v_1+v_2}{2} } }}
where v_1 and v_2 are the shape parameters dfn and dfd and \Gamma is the gamma function,
{\Gamma (a)} = {\int}_{0}^{\infty}{t^{a-1} e^{-t } \it dt}

See Also