Evaluates the noncentral beta cumulative probability distribution function
(CDF).
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralBeta(
double x,
double shape1,
double shape2,
double lambda
)
Public Shared Function NoncentralBeta (
x As Double,
shape1 As Double,
shape2 As Double,
lambda As Double
) As Double
public:
static double NoncentralBeta(
double x,
double shape1,
double shape2,
double lambda
)
static member NoncentralBeta :
x : float *
shape1 : float *
shape2 : float *
lambda : float -> float
Parameters
- x
- Type: SystemDouble
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: SystemDouble
A double scalar value representing the first shape
parameter. shape1 must be positive.
- shape2
- Type: SystemDouble
A double scalar value representing the second shape
parameter. shape2 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 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.
See Also