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:

java.io.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:

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

Field Summary

Fields

Modifier and Type	Field and Description
static 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 double	scale The scale parameter.
private static long	serialVersionUID Serializable version identifier.
private double	shape The shape parameter.
private double	solverAbsoluteAccuracy Inverse cumulative probability accuracy.

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

random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

Constructors

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

Method Summary

Methods

Modifier and Type	Method and Description
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.
double	logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point x.

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

serialVersionUID

private static final long serialVersionUID

Serializable version identifier.

See Also:

Constant Field Values

shape

private final double shape

The shape parameter.

scale

private final double scale

The scale parameter.

solverAbsoluteAccuracy

private final double solverAbsoluteAccuracy

Inverse cumulative probability accuracy.

numericalMean

private double numericalMean

Cached numerical mean

numericalMeanIsCalculated

private boolean numericalMeanIsCalculated

Whether or not the numerical mean has been calculated

numericalVariance

private double numericalVariance

Cached numerical variance

numericalVarianceIsCalculated

private boolean numericalVarianceIsCalculated

Whether or not the numerical variance has been calculated

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.

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 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

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(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