Evaluates the noncentral beta cumulative probability distribution function
(CDF).
Namespace:
Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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public static double NoncentralBeta( double x, double shape1, double shape2, double lambda ) |
Visual Basic (Declaration) |
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Public Shared Function NoncentralBeta ( _ x As Double, _ shape1 As Double, _ shape2 As Double, _ lambda As Double _ ) As Double |
Visual C++ |
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public: static double NoncentralBeta( double x, double shape1, double shape2, double lambda ) |
Parameters
- x
- Type: System..::.Double
A double scalar value representing the argument at which the function is to be evaluated. x must be nonnegative and less than or equal to 1.
- shape1
- Type: System..::.Double
A double scalar value representing the first shape parameter. shape1 must be positive.
- shape2
- Type: System..::.Double
A double scalar value representing the second shape parameter. shape2 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 probability that a noncentral beta random variable takes a value less than or equal to x.Remarks
The noncentral beta distribution is a generalization of the beta
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 beta-distributed random variable and
is a noncentral F-distributed random variable. The CDF for
noncentral beta variable X can thus be simply defined in
terms of the noncentral F CDF:
where is the noncentral beta CDF with
= x, =
shape1, =
shape2, and noncentrality parameter = lambda; is the noncentral
F CDF with argument f, numerator and denominator degrees of
freedom and respectively, and noncentrality parameter ; and:
(See documentation for class Cdf method NoncentralF
for a discussion of how the noncentral F CDF is defined and
calculated.)
With a noncentrality parameter of zero, the noncentral beta distribution is the same as the beta distribution.