CdfNoncentralstudentsT Method |
Evaluates the noncentral Student's t cumulative probability
distribution function.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralstudentsT(
double t,
int idf,
double delta
)
Public Shared Function NoncentralstudentsT (
t As Double,
idf As Integer,
delta As Double
) As Double
public:
static double NoncentralstudentsT(
double t,
int idf,
double delta
)
static member NoncentralstudentsT :
t : float *
idf : int *
delta : float -> float
Parameters
- t
- Type: SystemDouble
A double scalar value representing the argument at which the
function is to be evaluated.
- idf
- Type: SystemInt32
An int scalar value representing the number of degrees of
freedom. This must be positive.
- delta
- Type: SystemDouble
A double scalar value representing the noncentrality
parameter.
Return Value
Type:
Double
A
double scalar value representing the probability that a
noncentral Student's
t random variable takes a value less
than or equal to
t.
Remarks
Method
Cdf.NoncentralstudentsT evaluates the distribution
function
F of a noncentral
t random variable with
idf degrees of freedom and noncentrality
parameter
delta; that is, with
,
, and
,
where
is the gamma function. The
value of the distribution function at the point
is the probability that the random variable takes a
value less than or equal to
.
The noncentral t random variable can be defined by the
distribution function above, or alternatively and equivalently, as
the ratio of a normal random variable and an independent
chi-squared random variable. If w has a normal distribution
with mean and variance equal to one,
has an independent chi-squared distribution
with degrees of freedom, and
then
has a noncentral
distribution with
degrees of freedom and
noncentrality parameter
.
The distribution function of the noncentral can also be expressed as a double integral involving a
normal density function (see, for example, Owen 1962, page 108).
The method Cdf.NoncentralstudentsT uses the method of Owen
(1962, 1965), which uses repeated integration by parts on that
alternate expression for the distribution function.
See Also