Top Description Fields Constructors Methods
org.apache.commons.math3.distribution

public Class WeibullDistribution

extends AbstractRealDistribution
Class Inheritance
Imports
org.apache.commons.math3.exception.NotStrictlyPositiveException, .OutOfRangeException, org.apache.commons.math3.exception.util.LocalizedFormats, org.apache.commons.math3.random.RandomGenerator, .Well19937c, org.apache.commons.math3.special.Gamma, org.apache.commons.math3.util.FastMath
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
Weibull distribution (Wikipedia), Weibull distribution (MathWorld)

Field Summary

Modifier and TypeField and Description
public static final double
DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

private double
numericalMean

Cached numerical mean

private boolean
numericalMeanIsCalculated

Whether or not the numerical mean has been calculated

private double
numericalVariance

Cached numerical variance

private boolean
numericalVarianceIsCalculated

Whether or not the numerical variance has been calculated

private final double
scale

The scale parameter.

private static final long
serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.
private final double
shape

The shape parameter.

private final double
solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.
Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
randomrandomDataSOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

AccessConstructor and Description
public
WeibullDistribution(double
Shape parameter.
alpha, double
Scale parameter.
beta)

Create a Weibull distribution with the given shape and scale and a location equal to zero.

public
WeibullDistribution(double
Shape parameter.
alpha, double
Scale parameter.
beta, double
Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
inverseCumAccuracy)

Create a Weibull distribution with the given shape, scale and inverse cumulative probability accuracy and a location equal to zero.

public
WeibullDistribution(RandomGenerator
Random number generator.
rng, double
Shape parameter.
alpha, double
Scale parameter.
beta)

Creates a Weibull distribution.

public
WeibullDistribution(RandomGenerator
Random number generator.
rng, double
Shape parameter.
alpha, double
Scale parameter.
beta, double
Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
inverseCumAccuracy)

Creates a Weibull distribution.

Method Summary

Modifier and TypeMethod and Description
protected double

Returns:

the mean of this distribution
calculateNumericalMean()

used by getNumericalMean()

protected double

Returns:

the variance of this distribution
calculateNumericalVariance()

used by getNumericalVariance()

public double
cumulativeProbability(double
the point at which the CDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).

public double
density(double
the point at which the PDF is evaluated
x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Returns the probability density function (PDF) of this distribution evaluated at the specified point x.

public double
getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Use this method to get the numerical value of the mean of this distribution.

public double
getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Use this method to get the numerical value of the variance of this distribution.

public double

Returns:

the scale parameter, beta.
getScale()

Access the scale parameter, beta.

public double

Returns:

the shape parameter, alpha.
getShape()

Access the shape parameter, alpha.

protected double

Returns:

the solver absolute accuracy.
getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.

public double

Returns:

lower bound of the support (always 0)
getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Access the lower bound of the support.

public double

Returns:

upper bound of the support (always Double.POSITIVE_INFINITY)
getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Access the upper bound of the support.

public double
inverseCumulativeProbability(double
the cumulative probability
p)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

Computes the quantile function of this distribution.

public boolean

Returns:

true
isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.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.

public boolean
isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Whether or not the lower bound of support is in the domain of the density function.

public boolean
isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Whether or not the upper bound of support is in the domain of the density function.

public double
logDensity(double
the point at which the PDF is evaluated
x)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:
cumulativeProbabilityprobabilityprobabilityreseedRandomGeneratorsamplesample

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACYback to summary
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since
2.1
numericalMeanback to summary
private double numericalMean

Cached numerical mean

numericalMeanIsCalculatedback to summary
private boolean numericalMeanIsCalculated

Whether or not the numerical mean has been calculated

numericalVarianceback to summary
private double numericalVariance

Cached numerical variance

numericalVarianceIsCalculatedback to summary
private boolean numericalVarianceIsCalculated

Whether or not the numerical variance has been calculated

scaleback to summary
private final double scale

The scale parameter.

serialVersionUIDback to summary
private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.

shapeback to summary
private final double shape

The shape parameter.

solverAbsoluteAccuracyback to summary
private final double solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.

Constructor Detail

WeibullDistributionback to summary
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 sample() and 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:double

Shape parameter.

beta:double

Scale parameter.

Exceptions
NotStrictlyPositiveException:
if alpha <= 0 or beta <= 0.
WeibullDistributionback to summary
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 sample() and 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:double

Shape parameter.

beta:double

Scale parameter.

inverseCumAccuracy:double

Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions
NotStrictlyPositiveException:
if alpha <= 0 or beta <= 0.
Since
2.1
WeibullDistributionback to summary
public WeibullDistribution(RandomGenerator rng, double alpha, double beta) throws NotStrictlyPositiveException

Creates a Weibull distribution.

Parameters
rng:RandomGenerator

Random number generator.

alpha:double

Shape parameter.

beta:double

Scale parameter.

Exceptions
NotStrictlyPositiveException:
if alpha <= 0 or beta <= 0.
Since
3.3
WeibullDistributionback to summary
public WeibullDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy) throws NotStrictlyPositiveException

Creates a Weibull distribution.

Parameters
rng:RandomGenerator

Random number generator.

alpha:double

Shape parameter.

beta:double

Scale parameter.

inverseCumAccuracy:double

Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions
NotStrictlyPositiveException:
if alpha <= 0 or beta <= 0.
Since
3.1

Method Detail

calculateNumericalMeanback to summary
protected double calculateNumericalMean()

used by getNumericalMean()

Returns:double

the mean of this distribution

calculateNumericalVarianceback to summary
protected double calculateNumericalVariance()

used by getNumericalVariance()

Returns:double

the variance of this distribution

cumulativeProbabilityback to summary
public double cumulativeProbability(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

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:double

the point at which the CDF is evaluated

Returns:double

the probability that a random variable with this distribution takes a value less than or equal to x

densityback to summary
public double density(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Doc from org.apache.commons.math3.distribution.RealDistribution.density.

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:double

the point at which the PDF is evaluated

Returns:double

the value of the probability density function at point x

getNumericalMeanback to summary
public double getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

the mean or Double.NaN if it is not defined

getNumericalVarianceback to summary
public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getScaleback to summary
public double getScale()

Access the scale parameter, beta.

Returns:double

the scale parameter, beta.

getShapeback to summary
public double getShape()

Access the shape parameter, alpha.

Returns:double

the shape parameter, alpha.

getSolverAbsoluteAccuracyback to summary
protected double getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.

Returns:double

the solver absolute accuracy.

Annotations
@Override
Since
2.1
getSupportLowerBoundback to summary
public double getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

lower bound of the support (always 0)

getSupportUpperBoundback to summary
public double getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:double

upper bound of the support (always Double.POSITIVE_INFINITY)

inverseCumulativeProbabilityback to summary
public double inverseCumulativeProbability(double p)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

Implements org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.inverseCumulativeProbability.

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.
Parameters
p:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

the cumulative probability

Returns:double

Doc from org.apache.commons.math3.distribution.RealDistribution.inverseCumulativeProbability.

the smallest p-quantile of this distribution (largest 0-quantile for p = 0)

Annotations
@Override
isSupportConnectedback to summary
public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

true

isSupportLowerBoundInclusiveback to summary
public boolean isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusiveback to summary
public boolean isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.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:boolean

true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

logDensityback to summary
public double logDensity(double x)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

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

Parameters
x:double

the point at which the PDF is evaluated

Returns:double

the logarithm of the value of the probability density function at point x

Annotations
@Override