Evaluates the inverse of the noncentral 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 NoncentralstudentsT(
	double p,
	int idf,
	double delta
)
Visual Basic (Declaration)
Public Shared Function NoncentralstudentsT ( _
	p As Double, _
	idf As Integer, _
	delta As Double _
) As Double
Visual C++
public:
static double NoncentralstudentsT(
	double p, 
	int idf, 
	double delta
)

Parameters

p
Type: System..::.Double
A double scalar value representing the probability for which the function is to be evaluated.
idf
Type: System..::.Int32
An int scalar value representing the number of degrees of freedom. This must be positive.
delta
Type: System..::.Double
A double scalar value representing the noncentrality parameter.

Return Value

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

Remarks

Method InvCdf.NoncentralstudentsT evaluates the inverse distribution function of a noncentral t random variable with idf degrees of freedom and noncentrality parameter delta; that is, with P=p , \nu=idf, \delta=delta , it determines t_{0}=InvCdf.NoncentralstudentsT(p, idf, delta), such that
P=\int_{-{\infty}}^{t_{0}}{\frac{\nu^{ \nu/2}e^{{-\delta^2}/2}}{{\sqrt{\pi}\Gamma\left(\nu/2\right)\left( \nu+x^2\right)}^{\left(\nu+1\right)/2}}}\sum\limits_{i=0}^\infty{ \Gamma\left(\left(\nu+i+1\right)/2\right)\left(\frac{\delta^i}{i!} \right)\left(\frac{2x^2}{\nu+x^2}\right)^{i/2}dx}
where \Gamma(\cdot) is the Gamma function. The probability that the random variable takes a value less than or equal to t_{0} is P. See Cdf.NoncentralstudentsT for an alternative definition in terms of normal and chi-squared random variables. The method InvCdf.NoncentralstudentsT uses bisection and modified regula falsi to invert the distribution function, which is evaluated using Cdf.NoncentralstudentsT.

See Also