Package org.apache.commons.math3.distribution

Class NakagamiDistribution

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:

  • Field Details

    • DEFAULT_INVERSE_ABSOLUTE_ACCURACY

      public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
      Default inverse cumulative probability accuracy.
      See Also:

  • Constructor Details

    • 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 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.

    • 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 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