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

Constructors
Modifier Constructor and Description
protected Studentst()
Make class non-instantiable but inheritable.
• ### Method Summary

Methods
Modifier and Type Method and Description
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.