umontreal.iro.lecuyer.probdist

Class StudentDistQuick

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.StudentDist

umontreal.iro.lecuyer.probdist.StudentDistQuick

All Implemented Interfaces:

Distribution

public class StudentDistQuick
extends StudentDist

Extends the class StudentDist for the Student t-distribution. Uses methods that are faster but less precise than StudentDist.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

Constructors

Constructor and Description
StudentDistQuick(int n) Constructs a StudentDistQuick object with n degrees of freedom.

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
static double	barF(int n, double x) Computes the complementary distribution function bar(F)(x).
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(int n, double x) Returns an approximation of the Student t-distribution function with n degrees of freedom.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(int n, double u) Returns an approximation of F-1(u), where F is the Student t-distribution function with n degrees of freedom.

Methods inherited from class umontreal.iro.lecuyer.probdist.StudentDist

cdf2, density, density, getInstanceFromMLE, getMean, getMean, getMLE, getN, getParams, getStandardDeviation, getStandardDeviation, getVariance, getVariance, setN, toString

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

StudentDistQuick

public StudentDistQuick(int n)

Constructs a StudentDistQuick object with n degrees of freedom.

Method Detail

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class StudentDist

Parameters:

x - value at which the distribution function is evaluated

Returns:

distribution function evaluated at x

barF

public double barF(double x)

Description copied from class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class StudentDist

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from class: ContinuousDistribution

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class StudentDist

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

cdf

public static double cdf(int n,
                         double x)

Returns an approximation of the Student t-distribution function with n degrees of freedom. Is very poor in the tails but good in the central part of the range.

barF

public static double barF(int n,
                          double x)

Computes the complementary distribution function bar(F)(x).

inverseF

public static double inverseF(int n,
                              double u)

Returns an approximation of F^-1(u), where F is the Student t-distribution function with n degrees of freedom. Gives at least 5 decimal digits of precision when n >= 3 . Uses exact formulae for n = 1 and n = 2.