CauchyDistribution
org.apache.commons.math3.distribution

Class CauchyDistribution

    • 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

      • CauchyDistribution

        public CauchyDistribution()
        Creates a Cauchy distribution with the median equal to zero and scale equal to one.
      • CauchyDistribution

        public CauchyDistribution(double median,                  double scale)
        Creates a Cauchy distribution using the given median and scale.
        Parameters:
        median - Median for this distribution.
        scale - Scale parameter for this distribution.
      • CauchyDistribution

        public CauchyDistribution(double median,                  double scale,                  double inverseCumAccuracy)
        Creates a Cauchy distribution using the given median and scale.
        Parameters:
        median - Median for this distribution.
        scale - Scale parameter for this distribution.
        inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
        Throws:
        NotStrictlyPositiveException - if scale <= 0.
      • CauchyDistribution

        public CauchyDistribution(RandomGenerator rng,                  double median,                  double scale)
        Creates a Cauchy distribution.
        Parameters:
        rng - Random number generator.
        median - Median for this distribution.
        scale - Scale parameter for this distribution.
        Throws:
        NotStrictlyPositiveException - if scale <= 0.
      • CauchyDistribution

        public CauchyDistribution(RandomGenerator rng,                  double median,                  double scale,                  double inverseCumAccuracy)
        Creates a Cauchy distribution.
        Parameters:
        rng - Random number generator.
        median - Median for this distribution.
        scale - Scale parameter for this distribution.
        inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
        Throws:
        NotStrictlyPositiveException - if scale <= 0.
    • Method Detail

      • 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
      • getMedian

        public double getMedian()
        Access the median.
        Returns:
        the median for this distribution.
      • getScale

        public double getScale()
        Access the scale parameter.
        Returns:
        the scale parameter for this distribution.
      • 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
      • getNumericalMean

        public double getNumericalMean()
        Use this method to get the numerical value of the mean of this distribution. The mean is always undefined no matter the parameters.
        Returns:
        mean (always Double.NaN)
      • getNumericalVariance

        public double getNumericalVariance()
        Use this method to get the numerical value of the variance of this distribution. The variance is always undefined no matter the parameters.
        Returns:
        variance (always Double.NaN)
      • 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}.

        The lower bound of the support is always negative infinity no matter the parameters.
        Returns:
        lower bound of the support (always 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}.

        The upper bound of the support is always positive infinity no matter the parameters.
        Returns:
        upper bound of the support (always 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. The support of this distribution is connected.
        Returns:
        true

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