Top Description Fields Constructors Methods
org.apache.commons.math3.distribution

public Class NakagamiDistribution

extends AbstractRealDistribution
Class Inheritance
Imports
org.apache.commons.math3.exception.NotStrictlyPositiveException, .NumberIsTooSmallException, org.apache.commons.math3.exception.util.LocalizedFormats, org.apache.commons.math3.random.RandomGenerator, .Well19937c, org.apache.commons.math3.special.Gamma, org.apache.commons.math3.util.FastMath
This class implements the Nakagami distribution.
Since
3.4
See Also
Nakagami Distribution (Wikipedia)

Field Summary

Modifier and TypeField and Description
public static final double
DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

private final double
inverseAbsoluteAccuracy

Inverse cumulative probability accuracy.

private final double
mu

The shape parameter.

private final double
omega

The scale parameter.

private static final long
serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.
Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
randomrandomDataSOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

AccessConstructor and Description
public
NakagamiDistribution(double
shape parameter
mu, double
scale parameter (must be positive)
omega)

Build a new instance.

public
NakagamiDistribution(double
shape parameter
mu, double
scale parameter (must be positive)
omega, double
the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
inverseAbsoluteAccuracy)

Build a new instance.

public
NakagamiDistribution(RandomGenerator
Random number generator
rng, double
shape parameter
mu, double
scale parameter (must be positive)
omega, double
the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
inverseAbsoluteAccuracy)

Build a new instance.

Method Summary

Modifier and TypeMethod and Description
public double
cumulativeProbability(double
the point at which the CDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).

public double
density(double
the point at which the PDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Returns the probability density function (PDF) of this distribution evaluated at the specified point x.

public double
getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

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

public double
getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

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

public double

Returns:

the scale parameter.
getScale()

Access the scale parameter, omega.

public double

Returns:

the shape parameter.
getShape()

Access the shape parameter, mu.

protected double
getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Returns the solver absolute accuracy for inverse cumulative computation.

public double
getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Access the lower bound of the support.

public double
getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Access the upper bound of the support.

public boolean
isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.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.

public boolean
isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Whether or not the lower bound of support is in the domain of the density function.

public boolean
isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Whether or not the upper bound of support is in the domain of the density function.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
cumulativeProbabilityinverseCumulativeProbabilitylogDensityprobabilityprobabilityreseedRandomGeneratorsamplesample

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACYback to summary
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

inverseAbsoluteAccuracyback to summary
private final double inverseAbsoluteAccuracy

Inverse cumulative probability accuracy.

muback to summary
private final double mu

The shape parameter.

omegaback to summary
private final double omega

The scale parameter.

serialVersionUIDback to summary
private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.

Constructor Detail

NakagamiDistributionback to summary
public NakagamiDistribution(double mu, double omega)

Build a new instance.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and 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:double

shape parameter

omega:double

scale parameter (must be positive)

Exceptions
NumberIsTooSmallException:
if mu < 0.5
NotStrictlyPositiveException:
if omega <= 0
NakagamiDistributionback to summary
public NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy)

Build a new instance.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and 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:double

shape parameter

omega:double

scale parameter (must be positive)

inverseAbsoluteAccuracy:double

the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions
NumberIsTooSmallException:
if mu < 0.5
NotStrictlyPositiveException:
if omega <= 0
NakagamiDistributionback to summary
public NakagamiDistribution(RandomGenerator rng, double mu, double omega, double inverseAbsoluteAccuracy)

Build a new instance.

Parameters
rng:RandomGenerator

Random number generator

mu:double

shape parameter

omega:double

scale parameter (must be positive)

inverseAbsoluteAccuracy:double

the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions
NumberIsTooSmallException:
if mu < 0.5
NotStrictlyPositiveException:
if omega <= 0

Method Detail

cumulativeProbabilityback to summary
public double cumulativeProbability(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

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:double

the point at which the CDF is evaluated

Returns:double

the probability that a random variable with this distribution takes a value less than or equal to x

densityback to summary
public double density(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Doc from org.apache.commons.math3.distribution.RealDistribution.density.

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:double

the point at which the PDF is evaluated

Returns:double

the value of the probability density function at point x

getNumericalMeanback to summary
public double getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

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

Returns:double

the mean or Double.NaN if it is not defined

getNumericalVarianceback to summary
public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

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

Returns:double

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

getScaleback to summary
public double getScale()

Access the scale parameter, omega.

Returns:double

the scale parameter.

getShapeback to summary
public double getShape()

Access the shape parameter, mu.

Returns:double

the shape parameter.

getSolverAbsoluteAccuracyback to summary
protected double getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Returns:double

the maximum absolute error in inverse cumulative probability estimates

Annotations
@Override
getSupportLowerBoundback to summary
public double getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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 <= x) > 0}.

Returns:double

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

getSupportUpperBoundback to summary
public double getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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 <= x) = 1}.

Returns:double

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

isSupportConnectedback to summary
public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

whether the support is connected or not

isSupportLowerBoundInclusiveback to summary
public boolean isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

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

isSupportUpperBoundInclusiveback to summary
public boolean isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

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