WeibullDistribution (Apache Commons Math 3.6.1 API)

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:
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.
- Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
  random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_INVERSE_ABSOLUTE_ACCURACY` Default inverse cumulative probability 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
- 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

Class WeibullDistribution

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

WeibullDistribution

WeibullDistribution

WeibullDistribution

WeibullDistribution

Method Detail

getShape

getScale

density

logDensity

cumulativeProbability

inverseCumulativeProbability

getSolverAbsoluteAccuracy

getNumericalMean

calculateNumericalMean

getNumericalVariance

calculateNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected