Package org.hipparchus.distribution.continuous

Class NakagamiDistribution

java.lang.Object

org.hipparchus.distribution.continuous.AbstractRealDistribution

org.hipparchus.distribution.continuous.NakagamiDistribution

All Implemented Interfaces:

Serializable, RealDistribution

public class NakagamiDistribution
extends AbstractRealDistribution

This class implements the Nakagami distribution.

See Also:

• Nakagami Distribution (Wikipedia)
• Serialized Form

Field Summary

Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution

DEFAULT_SOLVER_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

Constructor	Description
NakagamiDistribution(double mu, double omega)	Build a new instance.
NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy)	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	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, omega.
double	getShape()	Access the shape parameter, mu.
double	getSupportLowerBound()	Access the lower bound of the support.
double	getSupportUpperBound()	Access the upper bound of the support.
boolean	isSupportConnected()	Use this method to get information about whether the support is connected, i.e.

Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution

getSolverAbsoluteAccuracy, inverseCumulativeProbability, logDensity, probability

Methods inherited from class java.lang.Object

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

Constructor Details

NakagamiDistribution

public NakagamiDistribution(double mu,
 double omega)
                     throws MathIllegalArgumentException

Build a new instance.

Parameters:

mu - shape parameter

omega - scale parameter (must be positive)

Throws:

MathIllegalArgumentException - if mu < 0.5

MathIllegalArgumentException - if omega <= 0

NakagamiDistribution

public NakagamiDistribution(double mu,
 double omega,
 double inverseAbsoluteAccuracy)
                     throws MathIllegalArgumentException

Build a new instance.

Parameters:

mu - shape parameter

omega - scale parameter (must be positive)

inverseAbsoluteAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to AbstractRealDistribution.DEFAULT_SOLVER_ABSOLUTE_ACCURACY).

Throws:

MathIllegalArgumentException - if mu < 0.5

MathIllegalArgumentException - if omega <= 0

Method Details

getShape

public double getShape()

Access the shape parameter, mu.

Returns:

the shape parameter.

getScale

public double getScale()

Access the scale parameter, omega.

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

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 <= 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 <= x) = 1}.

Returns:

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

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