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

Class LaplaceDistribution

java.lang.Object

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

All Implemented Interfaces:

ProbabilityDistribution<Double>

public class LaplaceDistribution
extends Object
implements ProbabilityDistribution<Double>

The Laplace distribution is a continuous probability distribution with probability density function $$ \begin{align*} f(x)=\frac{1}{2b}e^{-\frac{|x-\mu|}{b}} \end{align*} $$ where $\mu$ is the location parameter and $b$ is the scale parameter. The cumulative distribution function and its inverse are defined as: $$ \begin{align*} F(x)&= \begin{cases} \frac{1}{2}e^{\frac{x-\mu}{b}} & \text{if } x < \mu\\ 1-\frac{1}{2}e^{-\frac{x-\mu}{b}} & \text{if } x\geq \mu \end{cases}\\ F^{-1}(p)&=\mu-b\text{ sgn}(p-0.5)\ln(1-2|p-0.5|) \end{align*} $$ Given a uniform random variable $U$ drawn from the interval $(-\frac{1}{2}, \frac{1}{2}]$, a Laplace-distributed random variable with parameters $\mu$ and $b$ is given by: $$ \begin{align*} X=\mu-b\text{ sgn}(U)\ln(1-2|U|) \end{align*} $$

Constructor Summary

Constructors

Constructor and Description
LaplaceDistribution(double mu, double b) Creates an instance.
LaplaceDistribution(double mu, double b, RandomEngine engine) Creates an instance.

Method Summary

Modifier and Type	Method and Description
boolean	equals(Object obj)
double	getB() Gets the scale parameter.
double	getCDF(Double x) Returns the cumulative distribution function for a value
double	getInverseCDF(Double p) Given a probability, return the value that returns this cdf
double	getMu() Gets the location parameter.
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

LaplaceDistribution

public LaplaceDistribution(double mu,
                           double b)

Creates an instance.

Parameters:

mu - The location parameter

b - The scale parameter, greater than zero

LaplaceDistribution

public LaplaceDistribution(double mu,
                           double b,
                           RandomEngine engine)

Creates an instance.

Parameters:

mu - The location parameter

b - The scale parameter, greater than zero

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

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

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

getMu

public double getMu()

Gets the location parameter.

Returns:

The location parameter

getB

public double getB()

Gets the scale parameter.

Returns:

The scale parameter

hashCode

public int hashCode()

Overrides:

hashCode in class Object

equals

public boolean equals(Object obj)

Overrides:

equals in class Object