ChiSquareDist (Java Libraries for Stochastic Simulation)

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

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ChiSquareDistQuick
```
public class ChiSquareDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the chi-square distribution with n degrees of freedom, where n is a positive integer. Its density is

f (x) = x^(n/2)-1e^-x/2/(2^n/2Γ(n/2)), for x > 0.
where Γ(x) is the gamma function defined in GammaDist. The chi-square distribution is a special case of the gamma distribution with shape parameter n/2 and scale parameter 1/2. Therefore, one can use the methods of GammaDist for this distribution.
The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.

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

Constructor Summary

Constructors
Constructor and Description

ChiSquareDist(int n)
Constructs a chi-square distribution with n degrees of freedom.

Constructors
Constructor and Description
`ChiSquareDist(int n)` Constructs a chi-square distribution with `n` degrees of freedom.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(int n, int d, double x)` Computes the complementary chi-square distribution function with n degrees of freedom, evaluated at x.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(int n, int d, double x)` Computes the chi-square distribution function with n degrees of freedom, evaluated at x.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(int n, double x)` Computes the density function for a chi-square distribution with n degrees of freedom.
`static ChiSquareDist`	`getInstanceFromMLE(double[] x, int m)` Creates a new instance of a chi-square distribution with parameter n estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int m)` Deprecated.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(int n)` Computes and returns the mean E[X] = n of the chi-square distribution with parameter n.
`static double[]`	`getMLE(double[] x, int m)` Estimates the parameter n of the chi-square distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1.
`static double[]`	`getMomentsEstimate(double[] x, int m)` Estimates and returns the parameter [hat(n)] of the chi-square distribution using the moments method based on the m observations in table x[i], i = 0, 1,…, m - 1.
`int`	`getN()` Returns the parameter n of this object.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(int n)` Returns the standard deviation of the chi-square distribution with parameter n.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(int n)` Returns the variance Var[X] = 2n of the chi-square distribution with parameter n.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(int n, double u)` Computes an approximation of F^-1(u), where F is the chi-square distribution with n degrees of freedom.
`void`	`setN(int n)` Sets the parameter n of 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
  - ChiSquareDist
```
public ChiSquareDist(int n)
```
    Constructs a chi-square distribution 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 for a chi-square distribution with n degrees of freedom.
  - cdf
```
public static double cdf(int n,
         int d,
         double x)
```
    Computes the chi-square distribution function with n degrees of freedom, evaluated at x. The method tries to return d decimals digits of precision, but there is no guarantee.
  - barF
```
public static double barF(int n,
          int d,
          double x)
```
    Computes the complementary chi-square distribution function with n degrees of freedom, evaluated at x. The method tries to return d decimals digits of precision, but there is no guarantee.
  - inverseF
```
public static double inverseF(int n,
              double u)
```
    Computes an approximation of F^-1(u), where F is the chi-square distribution with n degrees of freedom. It gives at least 6 decimal digits of precision, except far in the tails (that is, for u < 10^-5 or u > 1 - 10^-5) where the function calls the method GammaDist.inverseF (n/2, 7, u) and multiplies the result by 2.0. To get better precision, one may call GammaDist.inverseF, but this method is slower than the current method, especially for large n. For instance, for n = 16, 1024, and 65536, the GammaDist.inverseF method is 2, 5, and 8 times slower, respectively, than the current method.
  - getMLE
```
public static double[] getMLE(double[] x,
              int m)
```
    Estimates the parameter n of the chi-square distribution using the maximum likelihood method, from the m observations x[i], i = 0, 1,…, m - 1. The estimate is returned in element 0 of the returned 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)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int m)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static ChiSquareDist getInstanceFromMLE(double[] x,
                               int m)
```
    Creates a new instance of a chi-square 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)
```
    Computes and returns the mean E[X] = n of the chi-square distribution with parameter n.
    
    Returns:
    the mean of the Chi-square distribution E[X] = n
  - getMomentsEstimate
```
public static double[] getMomentsEstimate(double[] x,
                          int m)
```
    Estimates and returns the parameter [hat(n)] of the chi-square distribution using the moments method based on the m observations in table 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
    
    Returns:
    returns the parameter [hat(n)]
  - getVariance
```
public static double getVariance(int n)
```
    Returns the variance Var[X] = 2n of the chi-square distribution with parameter n.
    
    Returns:
    the variance of the chi-square distribution VarX] = 2n
  - getStandardDeviation
```
public static double getStandardDeviation(int n)
```
    Returns the standard deviation of the chi-square distribution with parameter n.
    
    Returns:
    the standard deviation of the chi-square distribution
  - getN
```
public int getN()
```
    Returns the parameter n of this object.
  - setN
```
public void setN(int n)
```
    Sets the parameter n of this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class ChiSquareDist

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

ChiSquareDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getMomentsEstimate

getVariance

getStandardDeviation

getN

setN

getParams

toString