Returns the inverse of the F cumulative probability distribution function.

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

Syntax

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

Parameters

p
Type: System..::.Double
A double, the probability for which the inverse of the F distribution function is to be evaluated. Argument p must be in the open interval (0.0, 1.0).
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 probability that an F random variable takes a value less than or equal to this returned value is p.

Remarks

Method InvCdf.F evaluates the inverse distribution function of a Snedecor's F random variable with dfn numerator degrees of freedom and dfd denominator degrees of freedom. The function is evaluated by making a transformation to a beta random variable and then using InvCdf.Beta. If X is an F variate with v_1 and v_2 degrees of freedom and Y=v_1X/ (v_2 + v_1X), then Y is a beta variate with parameters p = v_1/2 and q = v_2/2 . If P \le 0.5, F uses this relationship directly, otherwise, it also uses a relationship between X random variables that can be expressed as follows, using f, which is the F cumulative distribution function:
{\rm F}(X,{\it dfn},{\it dfd})=1-{\rm F} (1/X,{\it dfd},{\it dfn})

See Also