org.apache.commons.math3.distribution

## Class WeibullDistribution

• ### 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
• ### 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()
protected double calculateNumericalVariance()
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
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)
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 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()
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()
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