StudentDist

Documentation of 'umontreal.iro.lecuyer.probdist.StudentDist' Java class StudentDist

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java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.StudentDist

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

StudentDistQuick
```
public class StudentDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the Student t-distribution with n degrees of freedom, where n is a positive integer. Its density is

f (x) = [Γ((n + 1)/2)/(Γ(n/2)(πn)^1/2)][1 + x²/n]^-(n+1)/2 for - ∞ < x < ∞,
where Γ(x) is the gamma function defined in GammaDist.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description

StudentDist(int n)
Constructs a StudentDist object with n degrees of freedom.

Constructors
Constructor and Description
`StudentDist(int n)` Constructs a `StudentDist` object with `n` degrees of freedom.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
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 v = bar(F)(x) with n degrees of freedom.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(int n, double x)` Computes the Student t-distribution function u = F(x) with n degrees of freedom.
`static double`	`cdf2(int n, int d, double x)` Deprecated.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(int n, double x)` Computes the density function of a Student t-distribution with n degrees of freedom.
`static StudentDist`	`getInstanceFromMLE(double[] x, int m)` Creates a new instance of a Student t-distribution with parameter n estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(int n)` Returns the mean E[X] = 0 of the Student t-distribution with parameter n.
`static double[]`	`getMLE(double[] x, int m)` Estimates the parameter n of the Student t-distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
`int`	`getN()` Returns the parameter n associated with this object.
`double[]`	`getParams()` Return a table containing the parameter of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(int n)` Computes and returns the standard deviation of the Student t-distribution with parameter n.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(int n)` Computes and returns the variance Var[X] = n/(n - 2) of the Student t-distribution with parameter n.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(int n, double u)` Returns the inverse x = F^-1(u) of Student t-distribution function with n degrees of freedom.
`void`	`setN(int n)` Sets the parameter n associated with this object.
`java.lang.String`	`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
  - StudentDist
```
public StudentDist(int n)
```
    Constructs a StudentDist object with n degrees of freedom.
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    
    x - value at which the density is evaluated
    
    Returns:
    
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    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 ContinuousDistribution
    
    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 ContinuousDistribution
    
    Parameters:
    
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    
    the standard deviation
  - density
```
public static double density(int n,
                             double x)
```
    Computes the density function of a Student t-distribution with n degrees of freedom.
  - cdf
```
public static double cdf(int n,
                         double x)
```
    Computes the Student t-distribution function u = F(x) with n degrees of freedom. Gives 13 decimal digits of precision for n <= 10⁵. For n > 10⁵, gives at least 6 decimal digits of precision everywhere, and at least 9 decimal digits of precision for all u > 10^-15.
  - cdf2
```
@Deprecated
public static double cdf2(int n,
                                      int d,
                                      double x)
```
    Deprecated.
    
    Same as cdf(n, x).
  - barF
```
public static double barF(int n,
                          double x)
```
    Computes the complementary distribution function v = bar(F)(x) with n degrees of freedom. Gives 13 decimal digits of precision for n <= 10⁵. For n > 10⁵, gives at least 6 decimal digits of precision everywhere, and at least 9 decimal digits of precision for all v > 10^-15.
  - inverseF
```
public static double inverseF(int n,
                              double u)
```
    Returns the inverse x = F^-1(u) of Student t-distribution function with n degrees of freedom. Gives 13 decimal digits of precision for n <= 10⁵, and at least 9 decimal digits of precision for n > 10⁵.
  - getMLE
```
public static double[] getMLE(double[] x,
                              int m)
```
    Estimates the parameter n of the Student t-distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1. The estimate is returned in a one-element array.
    
    Parameters:
    
    x - the list of observations to use to evaluate parameters
    
    m - the number of observations to use to evaluate parameters
    
    Returns:
    
    returns the parameter [hat(n)]
  - getInstanceFromMLE
```
public static StudentDist getInstanceFromMLE(double[] x,
                                             int m)
```
    Creates a new instance of a Student t-distribution with parameter n estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.
    
    Parameters:
    
    x - the list of observations to use to evaluate parameters
    
    m - the number of observations to use to evaluate parameters
  - getMean
```
public static double getMean(int n)
```
    Returns the mean E[X] = 0 of the Student t-distribution with parameter n.
    
    Returns:
    
    the mean of the Student t-distribution E[X] = 0
  - getVariance
```
public static double getVariance(int n)
```
    Computes and returns the variance Var[X] = n/(n - 2) of the Student t-distribution with parameter n.
    
    Returns:
    
    the variance of the Student t-distribution Var[X] = n/(n - 2)
  - getStandardDeviation
```
public static double getStandardDeviation(int n)
```
    Computes and returns the standard deviation of the Student t-distribution with parameter n.
    
    Returns:
    
    the standard deviation of the Student t-distribution
  - getN
```
public int getN()
```
    Returns the parameter n associated with this object.
  - setN
```
public void setN(int n)
```
    Sets the parameter n associated with this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameter of the current distribution.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

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Class StudentDist

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

StudentDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

cdf2

barF

inverseF

getMLE

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getN

setN

getParams

toString