Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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public static double NoncentralF( double f, double df1, double df2, double lambda ) |
Visual Basic (Declaration) |
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Public Shared Function NoncentralF ( _ f As Double, _ df1 As Double, _ df2 As Double, _ lambda As Double _ ) As Double |
Visual C++ |
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public: static double NoncentralF( double f, double df1, double df2, double lambda ) |
Parameters
- f
- Type: System..::.Double
A double value representing the argument at which the function is to be evaluated. f must be nonnegative.
- df1
- Type: System..::.Double
A double value representing the number of numerator degrees of freedom. df1 must be positive.
- df2
- Type: System..::.Double
A double value representing the number of denominator degrees of freedom. df2 must be positive.
- lambda
- Type: System..::.Double
A double value representing the noncentrality parameter. lambda must be nonnegative.
Return Value
A 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 :