org.apache.commons.math4.distribution

Class NakagamiDistribution

• Nested classes/interfaces inherited from interface org.apache.commons.math4.distribution.RealDistribution

RealDistribution.Sampler
• Field Summary

Fields
Modifier and Type Field and Description
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
• Fields inherited from class org.apache.commons.math4.distribution.AbstractRealDistribution

SOLVER_DEFAULT_ABSOLUTE_ACCURACY
• Constructor Summary

Constructors
Constructor and Description
NakagamiDistribution(double mu, double omega)
Creates a distribution.
NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy)
Creates a distribution.
• Method Summary

All Methods
Modifier and Type Method and 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.
protected double getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation.
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.apache.commons.math4.distribution.AbstractRealDistribution

createSampler, inverseCumulativeProbability, logDensity, probability, probability, sample
• Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• Field Detail

• DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
Constant Field Values
• Constructor Detail

• NakagamiDistribution

public NakagamiDistribution(double mu,
double omega)
Creates a distribution.
Parameters:
mu - shape parameter
omega - scale parameter (must be positive)
Throws:
NumberIsTooSmallException - if mu < 0.5
NotStrictlyPositiveException - if omega <= 0
• NakagamiDistribution

public NakagamiDistribution(double mu,
double omega,
double inverseAbsoluteAccuracy)
Creates a distribution.
Parameters:
mu - shape parameter
omega - scale parameter (must be positive)
inverseAbsoluteAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NumberIsTooSmallException - if mu < 0.5
NotStrictlyPositiveException - if omega <= 0
• Method Detail

• 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.
• getSolverAbsoluteAccuracy

protected double 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.
Overrides:
getSolverAbsoluteAccuracy in class AbstractRealDistribution
Returns:
the maximum absolute error in inverse cumulative probability estimates
• 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