Evaluates the inverse of the noncentral beta 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 NoncentralBeta( double p, double shape1, double shape2, double lambda ) |
Visual Basic (Declaration) |
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Public Shared Function NoncentralBeta ( _ p As Double, _ shape1 As Double, _ shape2 As Double, _ lambda As Double _ ) As Double |
Visual C++ |
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public: static double NoncentralBeta( double p, double shape1, double shape2, double lambda ) |
Parameters
- p
- Type: System..::.Double
A double scalar value representing the probability for which the inverse of the noncentral beta cumulative distribution function is to be evaluated. p must be non-negative and less than or equal to one.
- 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 be nonnegative.
Return Value
A double scalar value representing the inverse of the noncentral beta distribution function evaluated at p. The probability that a noncentral beta random variable takes a value less than or equal to NoncentralBeta 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 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.)
Method InvCdf.NoncentralBeta evaluates
by first evaluating: and then solving for x using . (See documentation for InvCdf.NoncentralF for a discussion of how the inverse noncentral F CDF is calculated.)