com.opengamma.strata.math.impl.statistics.distribution

Class ChiSquareDistribution

java.lang.Object

com.opengamma.strata.math.impl.statistics.distribution.ChiSquareDistribution

All Implemented Interfaces:

ProbabilityDistribution<Double>

public class ChiSquareDistribution
extends Object
implements ProbabilityDistribution<Double>

A $\chi^2$ distribution with $k$ degrees of freedom is the distribution of the sum of squares of $k$ independent standard normal random variables with cdf and inverse cdf $$ \begin{align*} F(x) &=\frac{\gamma\left(\frac{k}{2}, \frac{x}{2}\right)}{\Gamma\left(\frac{k}{2}\right)}\\ F^{-1}(p) &= 2\gamma^{-1}\left(\frac{k}{2}, p\right) \end{align*} $$ where $\gamma(y, z)$ is the lower incomplete Gamma function and $\Gamma(y)$ is the Gamma function. The pdf is given by: $$ \begin{align*} f(x)=\frac{x^{\frac{k}{2}-1}e^{-\frac{x}{2}}}{2^{\frac{k}{2}}\Gamma\left(\frac{k}{2}\right)} \end{align*} $$

Constructor Summary

Constructors

Constructor and Description
ChiSquareDistribution(double degrees) Creates an instance.
ChiSquareDistribution(double degrees, RandomEngine engine) Creates an instance.

Method Summary

Modifier and Type	Method and Description
boolean	equals(Object obj)
double	getCDF(Double x) Returns the cumulative distribution function for a value
double	getDegreesOfFreedom() Gets the degrees of freedom.
double	getInverseCDF(Double p) Given a probability, return the value that returns this cdf
double	getPDF(Double x) Return the probability density function for a value
int	hashCode()
double	nextRandom()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ChiSquareDistribution

public ChiSquareDistribution(double degrees)

Creates an instance.

Parameters:

degrees - The degrees of freedom of the distribution, not less than one

ChiSquareDistribution

public ChiSquareDistribution(double degrees,
                             RandomEngine engine)

Creates an instance.

Parameters:

degrees - The degrees of freedom of the distribution, not less than one

engine - A uniform random number generator, not null

Method Detail

getCDF

public double getCDF(Double x)

Returns the cumulative distribution function for a value

Specified by:

getCDF in interface ProbabilityDistribution<Double>

Parameters:

x - The value, not null

Returns:

The cdf

getPDF

public double getPDF(Double x)

Return the probability density function for a value

Specified by:

getPDF in interface ProbabilityDistribution<Double>

Parameters:

x - The value, not null

Returns:

The pdf

getInverseCDF

public double getInverseCDF(Double p)

Given a probability, return the value that returns this cdf

Specified by:

getInverseCDF in interface ProbabilityDistribution<Double>

Parameters:

p - The probability, not null. $0 \geq p \geq 1$

Returns:

The inverse cdf

nextRandom

public double nextRandom()

Specified by:

nextRandom in interface ProbabilityDistribution<Double>

Returns:

The next random number from this distribution

getDegreesOfFreedom

public double getDegreesOfFreedom()

Gets the degrees of freedom.

Returns:

The number of degrees of freedom

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object