Evaluates the Student's t cumulative probability distribution
function.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double StudentsT(
double t,
double df
)
Public Shared Function StudentsT (
t As Double,
df As Double
) As Double
public:
static double StudentsT(
double t,
double df
)
static member StudentsT :
t : float *
df : float -> float
Parameters
- t
- Type: SystemDouble
A double scalar value representing the argument at which the
function is to be evaluated.
- df
- Type: SystemDouble
A double scalar value representing the number of degrees of
freedom. This must be at least one.
Return Value
Type:
Double
A
double scalar value representing the probability that a
Student's t random variable takes a value less than or equal to
t.
Remarks
Method
Cdf.StudentsT evaluates the distribution function of a
Student's
t random variable with
df
degrees of freedom. If the square of
t is
greater than or equal to
df, the relationship of
a
t to an
f random variable (and
subsequently, to a beta random variable) is exploited, and routine
Cdf.Beta is used. Otherwise, the method described by Hill (1970)
is used. If
df is not an integer, if
df is greater than 19, or if
df is greater than 200, a Cornish-Fisher
expansion is used to evaluate the distribution function. If
df is less than 20 and
is less than 2.0, a trigonometric series (see
Abramowitz and Stegun 1964, equations 26.7.3 and 26.7.4, with some
rearrangement) is used. For the remaining cases, a series given by
Hill (1970) that converges well for large values of
t is used.
For greater right tail accuracy, see
Cdf.ComplementaryStudentsT.
See Also