org.apache.commons.math.distribution

## Class WeibullDistributionImpl

- java.lang.Object
- - org.apache.commons.math.distribution.AbstractDistribution
  - - org.apache.commons.math.distribution.AbstractContinuousDistribution
    - - org.apache.commons.math.distribution.WeibullDistributionImpl

All Implemented Interfaces:
  Serializable, ContinuousDistribution, Distribution, WeibullDistribution

    public class WeibullDistributionImpl
    extends AbstractContinuousDistribution
    implements WeibullDistribution, Serializable

Default implementation of `WeibullDistribution`.

Since:
  1.1
Version:
  $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
See Also:
  Serialized Form

### Field Summary

Fields
`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.math.distribution.AbstractContinuousDistribution

`randomData`

### Constructor Summary

Constructors
Constructor and Description
`WeibullDistributionImpl(double alpha, double beta)` Creates weibull distribution with the given shape and scale and a location equal to zero.
`WeibullDistributionImpl(double alpha, double beta, double inverseCumAccuracy)` Creates weibull distribution with the given shape, scale and inverse cumulative probability accuracy and a location equal to zero.

### Method Summary

Methods
`protected double` `calculateNumericalMean()` Calculates the mean.
`private double` `calculateNumericalVariance()` Calculates the variance.
`double` `cumulativeProbability(double x)` For this distribution, X, this method returns P(X < `x`).
`double` `density(double x)` Returns the probability density for a particular point.
`protected double` `getDomainLowerBound(double p)` Access the domain value lower bound, based on `p`, used to bracket a CDF root.
`protected double` `getDomainUpperBound(double p)` Access the domain value upper bound, based on `p`, used to bracket a CDF root.
`protected double` `getInitialDomain(double p)` Access the initial domain value, based on `p`, used to bracket a CDF root.
`double` `getNumericalMean()` Returns the mean of the distribution.
`double` `getNumericalVariance()` Returns the variance of the distribution.
`double` `getScale()` Access the scale parameter.
`double` `getShape()` Access the shape parameter.
`protected double` `getSolverAbsoluteAccuracy()` Return the absolute accuracy setting of the solver used to estimate inverse cumulative probabilities.
`double` `getSupportLowerBound()` Returns the lower bound of the support for the distribution.
`double` `getSupportUpperBound()` Returns the upper bound of the support for the distribution.
`private void` `invalidateParameterDependentMoments()` Invalidates the cached mean and variance.
`double` `inverseCumulativeProbability(double p)` For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.
`void` `setScale(double beta)` Deprecated. as of 2.1 (class will become immutable in 3.0)
`private void` `setScaleInternal(double beta)` Modify the scale parameter.
`void` `setShape(double alpha)` Deprecated. as of 2.1 (class will become immutable in 3.0)
`private void` `setShapeInternal(double alpha)` Modify the shape parameter.

### Methods inherited from class org.apache.commons.math.distribution.AbstractContinuousDistribution

`reseedRandomGenerator, sample, sample`

### Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

`cumulativeProbability`

### Methods inherited from class java.lang.Object

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

### Methods inherited from interface org.apache.commons.math.distribution.Distribution

`cumulativeProbability`

### 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 double shape

The shape parameter.

#### scale

    private 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

#### WeibullDistributionImpl

    public WeibullDistributionImpl(double alpha,
                           double beta)

Creates weibull distribution with the given shape and scale and a location equal to zero.

Parameters:
  `alpha` - the shape parameter.
  `beta` - the scale parameter.

#### WeibullDistributionImpl

    public WeibullDistributionImpl(double alpha,
                           double beta,
                           double inverseCumAccuracy)

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

Parameters:
  `alpha` - the shape parameter.
  `beta` - the scale parameter.
  `inverseCumAccuracy` - the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`)
Since:
  2.1

### Method Detail

#### cumulativeProbability

    public double cumulativeProbability(double x)

For this distribution, X, this method returns P(X < `x`).

Specified by:
  `cumulativeProbability` in interface `Distribution`
Parameters:
  `x` - the value at which the CDF is evaluated.
Returns:
  CDF evaluated at `x`.

#### getShape

    public double getShape()

Access the shape parameter.

Specified by:
  `getShape` in interface `WeibullDistribution`
Returns:
  the shape parameter.

#### getScale

    public double getScale()

Access the scale parameter.

Specified by:
  `getScale` in interface `WeibullDistribution`
Returns:
  the scale parameter.

#### density

    public double density(double x)

Returns the probability density for a particular point.

Overrides:
  `density` in class `AbstractContinuousDistribution`
Parameters:
  `x` - The point at which the density should be computed.
Returns:
  The pdf at point x.
Since:
  2.1

#### inverseCumulativeProbability

    public double inverseCumulativeProbability(double p)

For this distribution, X, this method returns the critical point x, such that P(X < x) = `p`.

Returns `Double.NEGATIVE_INFINITY` for p=0 and `Double.POSITIVE_INFINITY` for p=1.

Specified by:
  `inverseCumulativeProbability` in interface `ContinuousDistribution`
Overrides:
  `inverseCumulativeProbability` in class `AbstractContinuousDistribution`
Parameters:
  `p` - the desired probability
Returns:
  x, such that P(X < x) = `p`
Throws:
  `IllegalArgumentException` - if `p` is not a valid probability.

#### setShape

    @Deprecated
    public void setShape(double alpha)

Deprecated. as of 2.1 (class will become immutable in 3.0)
Modify the shape parameter.

Specified by:
  `setShape` in interface `WeibullDistribution`
Parameters:
  `alpha` - the new shape parameter value.

#### setShapeInternal

    private void setShapeInternal(double alpha)

Modify the shape parameter.

Parameters:
  `alpha` - the new shape parameter value.

#### setScale

    @Deprecated
    public void setScale(double beta)

Deprecated. as of 2.1 (class will become immutable in 3.0)
Modify the scale parameter.

Specified by:
  `setScale` in interface `WeibullDistribution`
Parameters:
  `beta` - the new scale parameter value.

#### setScaleInternal

    private void setScaleInternal(double beta)

Modify the scale parameter.

Parameters:
  `beta` - the new scale parameter value.

#### getDomainLowerBound

    protected double getDomainLowerBound(double p)

Access the domain value lower bound, based on `p`, used to bracket a CDF root. This method is used by `inverseCumulativeProbability(double)` to find critical values.

Specified by:
  `getDomainLowerBound` in class `AbstractContinuousDistribution`
Parameters:
  `p` - the desired probability for the critical value
Returns:
  domain value lower bound, i.e. P(X < lower bound) < `p`

#### getDomainUpperBound

    protected double getDomainUpperBound(double p)

Access the domain value upper bound, based on `p`, used to bracket a CDF root. This method is used by `inverseCumulativeProbability(double)` to find critical values.

Specified by:
  `getDomainUpperBound` in class `AbstractContinuousDistribution`
Parameters:
  `p` - the desired probability for the critical value
Returns:
  domain value upper bound, i.e. P(X < upper bound) > `p`

#### getInitialDomain

    protected double getInitialDomain(double p)

Access the initial domain value, based on `p`, used to bracket a CDF root. This method is used by `inverseCumulativeProbability(double)` to find critical values.

Specified by:
  `getInitialDomain` in class `AbstractContinuousDistribution`
Parameters:
  `p` - the desired probability for the critical value
Returns:
  initial domain value

#### getSolverAbsoluteAccuracy

    protected double getSolverAbsoluteAccuracy()

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

Overrides:
  `getSolverAbsoluteAccuracy` in class `AbstractContinuousDistribution`
Returns:
  the solver absolute accuracy
Since:
  2.1

#### getSupportLowerBound

    public double getSupportLowerBound()

Returns the lower bound of the support for the distribution. The lower bound of the support is always 0 no matter the parameters.

Returns:
  lower bound of the support (always 0)
Since:
  2.2

#### getSupportUpperBound

    public double getSupportUpperBound()

Returns the upper bound of the support for the distribution. The upper bound of the support is always positive infinity no matter the parameters.

Returns:
  upper bound of the support (always Double.POSITIVE_INFINITY)
Since:
  2.2

#### calculateNumericalMean

    protected double calculateNumericalMean()

Calculates the mean. The mean is `scale * Gamma(1 + (1 / shape))` where `Gamma(...)` is the Gamma-function

Returns:
  the mean
Since:
  2.2

#### calculateNumericalVariance

    private double calculateNumericalVariance()

Calculates the variance. The variance is `scale^2 * Gamma(1 + (2 / shape)) - mean^2` where `Gamma(...)` is the Gamma-function

Returns:
  the variance
Since:
  2.2

#### getNumericalMean

    public double getNumericalMean()

Returns the mean of the distribution.

Returns:
  the mean or Double.NaN if it's not defined
Since:
  2.2

#### getNumericalVariance

    public double getNumericalVariance()

Returns the variance of the distribution.

Returns:
  the variance (possibly Double.POSITIVE_INFINITY as for certain cases in `TDistributionImpl`) or Double.NaN if it's not defined
Since:
  2.2

#### invalidateParameterDependentMoments

    private void invalidateParameterDependentMoments()

Invalidates the cached mean and variance.