edu.northwestern.at.utils.math.distributions
Class Studentst

java.lang.Object
  edu.northwestern.at.utils.math.distributions.Studentst

public class Studentst
extends java.lang.Object

Student's t distribution functions.

Constructor Summary

protected

Studentst() Make class non-instantiable but inheritable.

Method Summary

static double	t(double t, double df) Compute probability for Student t distribution.
static double	tInverse(double p, double df) Compute percentage point for Student t distribution.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Studentst

protected Studentst()

Make class non-instantiable but inheritable.

Method Detail

t

public static double t(double t,
                       double df)
                throws java.lang.IllegalArgumentException

Compute probability for Student t distribution.

Parameters:

t - Percentage point of Student t distribution

df - Degrees of freedom

Returns:

The corresponding probability for the Student t distribution.

Throws:

java.lang.IllegalArgumentException - if df <= 0

The probability is computed using the following relationship between the incomplete beta distribution and Student's t:

tprob(t) = incompleteBeta( df/(df*t*t), df/2, 0.5 )

The result is accurate to about 14 decimal digits.

tInverse

public static double tInverse(double p,
                              double df)
                       throws java.lang.ArithmeticException,
                              java.lang.IllegalArgumentException

Compute percentage point for Student t distribution.

Parameters:

p - Probability level for percentage point

df - Degrees of freedom

Returns:

The corresponding percentage point of the Student t distribution.

Throws:

java.lang.IllegalArgumentException - p < 0 or p > 1 or df <= 0

java.lang.ArithmeticException - if incomplete beta evaluation fails

The percentage point is computed using the inverse incomplete beta distribution. This allows for fractional degrees of freedom.