Cdf.InverseNoncentralstudentsT Method

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

public static double InverseNoncentralstudentsT(
   double p,
   int idf,
   double delta
);

Parameters

p: A double scalar value representing the probability for which the function is to be evaluated.
idf: An int scalar value representing the number of degrees of freedom. This must be positive.
delta: 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 InverseNoncentralstudentsT evaluates the inverse distribution function of a noncentral t random variable with idf degrees of freedom and noncentrality parameter delta; that is, with , $\nu = idf$ , $\delta = delta$ , it determines $t_{0} =$ InverseNoncentralstudentsT(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 NoncentralstudentsT for an alternative definition in terms of normal and chi-squared random variables. The method InverseNoncentralstudentsT uses bisection and modified regula falsi to invert the distribution function, which is evaluated using NoncentralstudentsT.

Cdf.InverseNoncentralstudentsT Method

Parameters

Return Value

Remarks

See Also