Evaluates the noncentral F probability density function.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralF(
double f,
double df1,
double df2,
double lambda
)
Public Shared Function NoncentralF (
f As Double,
df1 As Double,
df2 As Double,
lambda As Double
) As Double
public:
static double NoncentralF(
double f,
double df1,
double df2,
double lambda
)
static member NoncentralF :
f : float *
df1 : float *
df2 : float *
lambda : float -> float
Parameters
- f
- Type: SystemDouble
A double value representing the argument
at which the function is to be evaluated. f
must be nonnegative.
- df1
- Type: SystemDouble
A double value representing the number
of numerator degrees of freedom. df1 must
be positive.
- df2
- Type: SystemDouble
A double value representing the number
of denominator degrees of freedom. df2 must
be positive.
- lambda
- Type: SystemDouble
A double value representing the noncentrality
parameter. lambda must be nonnegative.
Return Value
Type:
DoubleA
double value representing the probability
density associated with a noncentral
F random
variable with value
f.
Remarks The noncentral F distribution is a generalization of the F
distribution. If is a noncentral chi-square
random variable with noncentrality parameter
and degrees of freedom, and
is a chi-square random variable with degrees
of freedom which is statistically independent of ,
then
is a noncentral
F-distributed random variable whose PDF is given by:
where
where
is the gamma function,
=
df1,
=
df2,
=
lambda,
and
f =
f.
With a noncentrality parameter of zero, the noncentral F
distribution is the same as the F distribution.
The efficiency of the calculation of the above series is enhanced by:
calculating each term in the series
recursively in terms of either the term
preceding it or the term following it, andinitializing the sum with the largest series term and adding the
subsequent terms in order of decreasing magnitude.
Special cases:
For :
For :
For :
See Also