InvCdfNoncentralBeta Method |
Evaluates the inverse of the noncentral beta cumulative
distribution function (CDF).
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralBeta(
double p,
double shape1,
double shape2,
double lambda
)
Public Shared Function NoncentralBeta (
p As Double,
shape1 As Double,
shape2 As Double,
lambda As Double
) As Double
public:
static double NoncentralBeta(
double p,
double shape1,
double shape2,
double lambda
)
static member NoncentralBeta :
p : float *
shape1 : float *
shape2 : float *
lambda : float -> float
Parameters
- p
- Type: SystemDouble
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: 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 be nonnegative.
Return Value
Type:
Double
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.)
See Also