Package org.hipparchus.distribution.continuous

Class CauchyDistribution

java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.CauchyDistribution
All Implemented Interfaces:
Serializable, RealDistribution
public class CauchyDistribution extends AbstractRealDistribution
Implementation of the Cauchy distribution.
See Also:

  • Constructor Details

    • 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) throws MathIllegalArgumentException
      Creates a Cauchy distribution.
      Parameters:
      median - Median for this distribution
      scale - Scale parameter for this distribution
      Throws:
      MathIllegalArgumentException - if scale <= 0

  • Method Details

    • 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

    • inverseCumulativeProbability

      public double inverseCumulativeProbability(double p) throws MathIllegalArgumentException
      Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
      • inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(X<=x) > 0} for p = 0.
      The default implementation returns Returns Double.NEGATIVE_INFINITY when p == 0 and Double.POSITIVE_INFINITY when p == 1.
      Specified by:
      inverseCumulativeProbability in interface RealDistribution
      Overrides:
      inverseCumulativeProbability in class AbstractRealDistribution
      Parameters:
      p - the cumulative probability
      Returns:
      the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
      Throws:
      MathIllegalArgumentException - if p < 0 or p > 1

    • 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)

    • 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