Package org.hipparchus.distribution.continuous

Class WeibullDistribution

java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.WeibullDistribution
All Implemented Interfaces:
Serializable, RealDistribution
public class WeibullDistribution extends AbstractRealDistribution
Implementation of the Weibull distribution. This implementation uses the two parameter form of the distribution defined by Weibull Distribution, equations (1) and (2).
See Also:

  • Constructor Details

    • WeibullDistribution

      public WeibullDistribution(double alpha, double beta) throws MathIllegalArgumentException
      Create a Weibull distribution with the given shape and scale.
      Parameters:
      alpha - Shape parameter.
      beta - Scale parameter.
      Throws:
      MathIllegalArgumentException - if alpha <= 0 or beta <= 0.

  • Method Details

    • getShape

      public double getShape()
      Access the shape parameter, alpha.
      Returns:
      the shape parameter, alpha.

    • getScale

      public double getScale()
      Access the scale parameter, beta.
      Returns:
      the scale parameter, beta.

    • 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

    • logDensity

      public double logDensity(double x)
      Returns the natural logarithm of 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. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of RealDistribution.density(double).

      The default implementation simply computes the logarithm of density(x).

      Specified by:
      logDensity in interface RealDistribution
      Overrides:
      logDensity in class AbstractRealDistribution
      Parameters:
      x - the point at which the PDF is evaluated
      Returns:
      the logarithm of 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

    • inverseCumulativeProbability

      public double inverseCumulativeProbability(double p)
      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 0 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)

    • getNumericalMean

      public double getNumericalMean()
      Use this method to get the numerical value of the mean of this distribution. The mean is scale * Gamma(1 + (1 / shape)), where Gamma() is the Gamma-function.
      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. The variance is scale^2 * Gamma(1 + (2 / shape)) - mean^2 where Gamma() is the Gamma-function.
      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}.

      The lower bound of the support is always 0 no matter the parameters.
      Returns:
      lower bound of the support (always 0)

    • 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