org.apache.commons.statistics.distribution

## Class ChiSquaredDistribution

• java.lang.Object
• org.apache.commons.statistics.distribution.ChiSquaredDistribution

• ### Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

ContinuousDistribution.Sampler
• ### Constructor Summary

Constructors
Constructor and Description
ChiSquaredDistribution(double degreesOfFreedom)
Creates a distribution.
• ### Method Summary

All Methods
Modifier and Type Method and Description
ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.
double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double getDegreesOfFreedom()
Access the number of degrees of freedom.
double getMean()
Gets the mean of this distribution.
double getSupportLowerBound()
Gets the lower bound of the support.
double getSupportUpperBound()
Gets the upper bound of the support.
double getVariance()
Gets the variance of this distribution.
double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution.
boolean isSupportConnected()
Indicates whether the support is connected, i.e.
double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
static double[] sample(int n, ContinuousDistribution.Sampler sampler)
Utility function for allocating an array and filling it with n samples generated by the given sampler.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

probability, probability
• ### Constructor Detail

• #### ChiSquaredDistribution

public ChiSquaredDistribution(double degreesOfFreedom)
Creates a distribution.
Parameters:
degreesOfFreedom - Degrees of freedom.
• ### Method Detail

• #### getDegreesOfFreedom

public double getDegreesOfFreedom()
Access the number of degrees of freedom.
Returns:
the degrees of freedom.
• #### density

public double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
Parameters:
x - Point at which the PDF is evaluated.
Returns:
the value of the probability density function at x.
• #### logDensity

public double logDensity(double x)
Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.
Parameters:
x - Point at which the PDF is evaluated.
Returns:
the logarithm of the value of the probability density function at x.
• #### cumulativeProbability

public double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
Parameters:
x - Point at which the CDF is evaluated.
Returns:
the probability that a random variable with this distribution takes a value less than or equal to x.
• #### getMean

public double getMean()
Gets the mean of this distribution. For k degrees of freedom, the mean is k.
Returns:
the mean, or Double.NaN if it is not defined.
• #### getVariance

public double getVariance()
Gets the variance of this distribution.
Returns:
2 * k, where k is the number of degrees of freedom.
• #### getSupportLowerBound

public double getSupportLowerBound()
Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. inf {x in R | P(X <= x) > 0}. The lower bound of the support is always 0 no matter the degrees of freedom.
Returns:
zero.
• #### getSupportUpperBound

public double getSupportUpperBound()
Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. inf {x in R | P(X <= x) = 1}. The upper bound of the support is always positive infinity no matter the degrees of freedom.
Returns:
Double.POSITIVE_INFINITY.
• #### isSupportConnected

public boolean isSupportConnected()
Indicates whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
Returns:
true
• #### createSampler

public ContinuousDistribution.Sampler createSampler(org.apache.commons.rng.UniformRandomProvider rng)
Creates a sampler.

Sampling algorithms:

• For 0 < degreesOfFreedom < 2:
Ahrens, J. H. and Dieter, U., Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing, 12, 223-246, 1974.
• For degreesOfFreedom >= 2:
Marsaglia and Tsang, A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, Volume 26 Issue 3, September, 2000.
Specified by:
createSampler in interface ContinuousDistribution
Parameters:
rng - Generator of uniformly distributed numbers.
Returns:
a sampler that produces random numbers according this distribution.
• #### inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
• inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
• inf{x in R | P(X<=x) > 0} for p = 0.
The default implementation returns
Specified by:
inverseCumulativeProbability in interface ContinuousDistribution
Parameters:
p - Cumulative probability.
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0).
• #### sample

public static double[] sample(int n,
ContinuousDistribution.Sampler sampler)
Utility function for allocating an array and filling it with n samples generated by the given sampler.
Parameters:
n - Number of samples.
sampler - Sampler.
Returns:
an array of size n.