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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.ChiSquareDist
public class ChiSquareDist
Extends the class ContinuousDistribution
for
the chi-square distribution with n degrees of freedom,
where n is a positive integer.
Its density is
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 |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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ChiSquareDist(int n)
Constructs a chi-square distribution with n degrees of freedom. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(int n,
int d,
double x)
Computes the complementary chi-square distribution function with n degrees of freedom. |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(int n,
int d,
double x)
Computes an approximation of the chi-square distribution function with n degrees of freedom. |
double |
density(double x)
Returns f (x), the density of X 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 in table x[i], i = 0, 1,…, m - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int m)
Estimates and returns the parameter [hat(n)] of the chi-square distribution using the maximum likelihood method based on the m observations in table x[i], i = 0, 1,…, m - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(int n)
Computes and returns the mean E[X] = n of the chi-square distribution with parameter n. |
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 |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(int n)
Computes and returns the standard deviation of the chi-square distribution with parameter n. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(int n)
Computes and returns the variance Var[X] = 2n of the chi-square distribution with parameter n. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
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. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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inverseBisection, inverseBrent |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public ChiSquareDist(int n)
Method Detail |
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public double density(double x)
ContinuousDistribution
density
in class ContinuousDistribution
x
- value at which the density is evaluated
public double cdf(double x)
Distribution
x
- value at which the distribution function is evaluated
public double barF(double x)
Distribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary distribution function is evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
u
- value in the interval (0, 1) for which the inverse
distribution function is evaluated
public double getMean()
Distribution
public double getVariance()
Distribution
public double getStandardDeviation()
Distribution
public static double density(int n, double x)
public static double cdf(int n, int d, double x)
GammaDist.cdf
(n/2, d, x/2)
instead, because it is faster and as accurate as the above approximation
for such n.
public static double barF(int n, int d, double x)
GammaDist.barF
(n/2, d, x/2)
for n > 350.
public static double inverseF(int n, double u)
public static ChiSquareDist getInstanceFromMLE(double[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(double[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameters
public static double getMean(int n)
public static double[] getMomentsEstimate(double[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameters
public static double getVariance(int n)
public static double getStandardDeviation(int n)
public int getN()
public void setN(int n)
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