Evaluates the inverse of the noncentral F cumulative distribution
function (CDF).
Namespace:
Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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public static double NoncentralF( double p, double dfn, double dfd, double lambda ) |
Visual Basic (Declaration) |
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Public Shared Function NoncentralF ( _ p As Double, _ dfn As Double, _ dfd As Double, _ lambda As Double _ ) As Double |
Visual C++ |
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public: static double NoncentralF( double p, double dfn, double dfd, double lambda ) |
Parameters
- p
- Type: System..::.Double
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: System..::.Double
A double scalar value representing the number of numerator degrees of freedom. dfn must be positive.
- dfd
- Type: System..::.Double
A double scalar value representing the number of denominator degrees of freedom. dfd must be positive.
- lambda
- Type: System..::.Double
A double scalar value representing the noncentrality parameter. lambda must nonnegative.
Return Value
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.