PdfNoncentralStudentsT Method |
Evaluates the noncentral Student's t probability density function.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double NoncentralStudentsT(
double t,
double df,
double delta
)
Public Shared Function NoncentralStudentsT (
t As Double,
df As Double,
delta As Double
) As Double
public:
static double NoncentralStudentsT(
double t,
double df,
double delta
)
static member NoncentralStudentsT :
t : float *
df : float *
delta : float -> float
Parameters
- t
- Type: SystemDouble
A double value representing the argument
at which the function is to be evaluated.
- df
- Type: SystemDouble
A double value representing the number
of degrees of freedom. df must be positive.
- delta
- Type: SystemDouble
A double value representing the
noncentrality parameter.
Return Value
Type:
Double
A
double value representing the probability
density associated with a noncentral Student's
t
random variable with value
t.
Remarks The noncentral Student's t-distribution is a generalization of
the Student's t-distribution. If is a
normally distributed random variable with unit variance and mean
and is a chi-square
random variable with degrees of freedom that is
statistically independent of , then
is a noncentral t-distributed random variable with
degrees of freedom and noncentrality parameter
, that is, with =
df, and = delta.
The probability density function for the noncentral t-distribution
is:
where
and t = t.
For noncentrality parameter = 0, the PDF
reduces to the (central) Student's t PDF:
and, for t = 0, the Pdf becomes:
See Also