Returns the inverse of the Student's t cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double StudentsT(
	double p,
	double df
)
Visual Basic (Declaration)
Public Shared Function StudentsT ( _
	p As Double, _
	df As Double _
) As Double
Visual C++
public:
static double StudentsT(
	double p, 
	double df
)

Parameters

p
Type: System..::.Double
A double scalar value representing the probability for which the inverse Student's t function is to be evaluated.
df
Type: System..::.Double
A double scalar value representing the number of degrees of freedom. This must be at least one.

Return Value

A double scalar value. The probability that a Student's t random variable takes a value less than or equal to this returned value is p.

Remarks

InvCdf.StudentsT evaluates the inverse distribution function of a Student's t random variable with df degrees of freedom. Let v = df. If v equals 1 or 2, the inverse can be obtained in closed form, if v is between 1 and 2, the relationship of a t to a beta random variable is exploited and InvCdf.Beta is used to evaluate the inverse; otherwise the algorithm of Hill (1970) is used. For small values of v greater than 2, Hill's algorithm inverts an integrated expansion in 1/(1+t^2/v) of the t density. For larger values, an asymptotic inverse Cornish-Fisher type expansion about normal deviates is used.

See Also