Package org.apache.commons.math3.distribution

Class LaplaceDistribution

java.lang.Object

org.apache.commons.math3.distribution.AbstractRealDistribution

org.apache.commons.math3.distribution.LaplaceDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class LaplaceDistribution
extends AbstractRealDistribution

This class implements the Laplace distribution.

Since:

3.4

See Also:

• Laplace distribution (Wikipedia)
• Serialized Form

Field Summary

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

Constructor	Description
LaplaceDistribution(double mu, double beta)	Build a new instance.
LaplaceDistribution(RandomGenerator rng, double mu, double beta)	Build a new instance.

Method Summary

Modifier and Type	Method	Description
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	getLocation()	Access the location parameter, mu.
double	getNumericalMean()	Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance()	Use this method to get the numerical value of the variance of this distribution.
double	getScale()	Access the scale parameter, beta.
double	getSupportLowerBound()	Access the lower bound of the support.
double	getSupportUpperBound()	Access the upper bound of the support.
double	inverseCumulativeProbability(double p)	Computes the quantile function of this distribution.
boolean	isSupportConnected()	Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
boolean	isSupportLowerBoundInclusive()	Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive()	Whether or not the upper bound of support is in the domain of the density function.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, getSolverAbsoluteAccuracy, logDensity, probability, probability, reseedRandomGenerator, sample, sample

Methods inherited from class java.lang.Object

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

Constructor Details

LaplaceDistribution

public LaplaceDistribution(double mu,
 double beta)

Build a new instance.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead.

Parameters:

mu - location parameter

beta - scale parameter (must be positive)

Throws:

NotStrictlyPositiveException - if beta <= 0

LaplaceDistribution

public LaplaceDistribution(RandomGenerator rng,
 double mu,
 double beta)

Build a new instance.

Parameters:

rng - Random number generator

mu - location parameter

beta - scale parameter (must be positive)

Throws:

NotStrictlyPositiveException - if beta <= 0

Method Details

getLocation

public double getLocation()

Access the location parameter, mu.

Returns:

the location parameter.

getScale

public double getScale()

Access the scale parameter, beta.

Returns:

the scale parameter.

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 - the point at which the PDF is evaluated

Returns:

the value of the probability density function at point 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 - the 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

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException

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(Xinvalid input: '<'=x) >= p} for 0 < p <= 1,
• inf{x in R | P(Xinvalid input: '<'=x) > 0} for p = 0.

The default implementation returns

• RealDistribution.getSupportLowerBound() for p = 0,
• RealDistribution.getSupportUpperBound() for p = 1.

Specified by:

inverseCumulativeProbability in interface RealDistribution

Overrides:

inverseCumulativeProbability in class AbstractRealDistribution

Parameters:

p - the cumulative probability

Returns:

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Throws:

OutOfRangeException - if p < 0 or p > 1

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution.

Returns:

the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution.

Returns:

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X invalid input: '<'= x) > 0}.

Returns:

lower bound of the support (might be Double.NEGATIVE_INFINITY)

getSupportUpperBound

public double getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X invalid input: '<'= x) = 1}.

Returns:

upper bound of the support (might be Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.

Returns:

whether the support is connected or not