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)

Version:

$Id: WeibullDistribution.java 7721 2013-02-14 14:07:13Z CardosoP $

See Also:

Weibull distribution (Wikipedia), Weibull distribution (MathWorld), Serialized Form

Field Summary

static double

DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

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

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.

WeibullDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy)
Creates a Weibull distribution.

Method Summary

protected double	calculateNumericalMean() used by getNumericalMean()
protected double	calculateNumericalVariance() used by getNumericalVariance()
double	cumulativeProbability(double x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
double	density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
double	getScale() Access the scale parameter, beta.
double	getShape() Access the shape parameter, alpha.
protected double	getSolverAbsoluteAccuracy() Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
double	getSupportLowerBound() Access the lower bound of the support.
double	getSupportUpperBound() Access the upper bound of the support.
double	inverseCumulativeProbability(double p) Computes the quantile function of this distribution.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
boolean	isSupportLowerBoundInclusive() Whether or not the lower bound of support is in the domain of the density function.
boolean	isSupportUpperBoundInclusive() Whether or not the upper bound of support is in the domain of the density function.

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

cumulativeProbability, probability, probability, reseedRandomGenerator, sample, sample

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since:

2.1

See Also:

Constant Field Values

Constructor Detail

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.

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.

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,
                           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 Detail

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

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

• RealDistribution.getSupportLowerBound() for p = 0,
• RealDistribution.getSupportUpperBound() for p = 1.

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 <= 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)

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