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

Class StudentTDistribution

java.lang.Object

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

All Implemented Interfaces:

ProbabilityDistribution<Double>

public class StudentTDistribution
extends Object
implements ProbabilityDistribution<Double>

Student's T-distribution is a continuous probability distribution with probability density function $$ \begin{align*} f(x) = \frac{\Gamma\left(\frac{\nu + 1}{2}\right)}{\sqrt{\nu\pi}\Gamma(\left(\frac{\nu}{2}\right)}\ left(1 + \frac{x^2}{\nu}\right)^{-\frac{1}{2}(\nu + 1)} \end{align*} $$ where $\nu$ is the number of degrees of freedom and $\Gamma$ is the Gamma function (GammaFunction).

Constructor Summary

Constructors

Constructor and Description
StudentTDistribution(double degFreedom)
StudentTDistribution(double degFreedom, RandomEngine engine)

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()
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

StudentTDistribution

public StudentTDistribution(double degFreedom)

Parameters:

degFreedom - The number of degrees of freedom, not negative or zero

StudentTDistribution

public StudentTDistribution(double degFreedom,
                            RandomEngine engine)

Parameters:

degFreedom - The number of degrees of freedom, not negative or zero

engine - A generator of uniform random numbers, 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

nextRandom

public double nextRandom()

Specified by:

nextRandom in interface ProbabilityDistribution<Double>

Returns:

The next random number from this distribution

getInverseCDF

public double getInverseCDF(Double p)

Given a probability, return the value that returns this cdf The inverse cdf is given by: $$ \begin{align*} F(P) &= \mathrm{sign}(p - \frac{1}{2})\sqrt{\frac{\nu}{x - 1}}\\ x &= B(2 \min(p, 1-p)) \end{align*} $$ where $B$ is the inverse incomplete Beta function (InverseIncompleteBetaFunction).

Specified by:

getInverseCDF in interface ProbabilityDistribution<Double>

Parameters:

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

Returns:

The inverse cdf

getDegreesOfFreedom

public double getDegreesOfFreedom()

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