Evaluates the inverse of the noncentral F cumulative distribution
function (CDF).
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralF(
double p,
double dfn,
double dfd,
double lambda
)
Public Shared Function NoncentralF (
p As Double,
dfn As Double,
dfd As Double,
lambda As Double
) As Double
public:
static double NoncentralF(
double p,
double dfn,
double dfd,
double lambda
)
static member NoncentralF :
p : float *
dfn : float *
dfd : float *
lambda : float -> float
Parameters
- p
- Type: SystemDouble
A double scalar value representing the probability for which
the inverse of the noncentral F cumulative distribution
function is to be evaluated. p must be
non-negative and less
than one.
- dfn
- Type: SystemDouble
A double scalar value representing the number of numerator
degrees of freedom. dfn must be positive.
- dfd
- Type: SystemDouble
A double scalar value representing the number of denominator
degrees of freedom. dfd must be positive.
- lambda
- Type: SystemDouble
A double scalar value representing the noncentrality
parameter. lambda must nonnegative.
Return Value
Type:
Double
A
double scalar value representing the inverse of the
noncentral
F distribution function evaluated at
p. The probability that a noncentral
F
random variable takes a value less than or equal to
InvCdf.NoncentralF(p, dfn, dfd, lambda) is
p.
Remarks
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 CDF is
given by:
where the probability density function
is given by:
where
is the Gamma
function,
=
dfn,
=
dfd,
=
lambda, and
is the probability that
.
Method InvCdf.NoncentralF evaluates
Method
InvCdf.NoncentralF uses bisection and modified regula
falsi search algorithms to invert the distribution function
, which is evaluated
using method
Cdf.NoncentralF. For sufficiently small
p, an accurate approximation of
can be used which requires no such
inverse search algorithms.
See Also