NakagamiDistribution (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.distribution.AbstractRealDistribution
- - org.apache.commons.math3.distribution.NakagamiDistribution

All Implemented Interfaces:

Serializable, RealDistribution
```
public class NakagamiDistribution
extends AbstractRealDistribution
```
This class implements the Nakagami distribution.

Since:

3.4

See Also:
Nakagami Distribution (Wikipedia), Serialized Form

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.math3.distribution.AbstractRealDistribution
  random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_INVERSE_ABSOLUTE_ACCURACY` Default inverse cumulative probability accuracy.

Constructor Summary

Constructors
Constructor and Description
`NakagamiDistribution(double mu, double omega)` Build a new instance.
`NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy)` Build a new instance.
`NakagamiDistribution(RandomGenerator rng, double mu, double omega, double inverseAbsoluteAccuracy)` Build a new instance.

Method Summary

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.
`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, inverseCumulativeProbability, logDensity, probability, probability, reseedRandomGenerator, sample, 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.
    
    See Also:
    Constant Field Values
- Constructor Detail
  - NakagamiDistribution
```
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 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 - 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)
```
    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 - 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
  - NakagamiDistribution
```
public NakagamiDistribution(RandomGenerator rng,
                    double mu,
                    double omega,
                    double inverseAbsoluteAccuracy)
```
    Build a new instance.
    
    Parameters:
    rng - Random number generator
    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)
  - 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

Class NakagamiDistribution

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

NakagamiDistribution

NakagamiDistribution

NakagamiDistribution

Method Detail

getShape

getScale

getSolverAbsoluteAccuracy

density

cumulativeProbability

getNumericalMean

getNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected