Package org.apache.commons.math3.distribution

Class WeibullDistribution

java.lang.Object
org.apache.commons.math3.distribution.AbstractRealDistribution
org.apache.commons.math3.distribution.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).
Since:
1.1 (changed to concrete class in 3.0)
See Also:

  • Field Details

    • DEFAULT_INVERSE_ABSOLUTE_ACCURACY

      public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
      Default inverse cumulative probability accuracy.
      Since:
      2.1
      See Also:

  • Constructor Details

    • WeibullDistribution

      public WeibullDistribution(double alpha, double beta) throws NotStrictlyPositiveException
      Create a Weibull distribution with the given shape and scale and a location equal to zero.

      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:
      alpha - Shape parameter.
      beta - Scale parameter.
      Throws:
      NotStrictlyPositiveException - if alpha <= 0 or beta <= 0.

    • WeibullDistribution

      public WeibullDistribution(double alpha, double beta, double inverseCumAccuracy)
      Create a Weibull distribution with the given shape, scale and inverse cumulative probability accuracy and a location equal to zero.

      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:
      alpha - Shape parameter.
      beta - Scale parameter.
      inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
      Throws:
      NotStrictlyPositiveException - if alpha <= 0 or beta <= 0.
      Since:
      2.1

    • WeibullDistribution

      public WeibullDistribution(RandomGenerator rng, double alpha, double beta) throws NotStrictlyPositiveException
      Creates a Weibull distribution.
      Parameters:
      rng - Random number generator.
      alpha - Shape parameter.
      beta - Scale parameter.
      Throws:
      NotStrictlyPositiveException - if alpha <= 0 or beta <= 0.
      Since:
      3.3

    • WeibullDistribution

      public WeibullDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy) throws NotStrictlyPositiveException
      Creates a Weibull distribution.
      Parameters:
      rng - Random number generator.
      alpha - Shape parameter.
      beta - Scale parameter.
      inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
      Throws:
      NotStrictlyPositiveException - if alpha <= 0 or beta <= 0.
      Since:
      3.1

  • 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).
      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(Xinvalid input: '<'=x) >= p} for 0 < p <= 1,
      • inf{x in R | P(Xinvalid input: '<'=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)

    • getSolverAbsoluteAccuracy

      protected double getSolverAbsoluteAccuracy()
      Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
      Overrides:
      getSolverAbsoluteAccuracy in class AbstractRealDistribution
      Returns:
      the solver absolute accuracy.
      Since:
      2.1

    • 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

    • calculateNumericalMean

      protected double calculateNumericalMean()
      used by getNumericalMean()
      Returns:
      the mean of this distribution

    • 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

    • calculateNumericalVariance

      protected double calculateNumericalVariance()
      used by getNumericalVariance()
      Returns:
      the variance of this distribution

    • 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}.

      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 invalid input: '<'= 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