org.apache.commons.math3.distribution

## Class WeibullDistribution

• ### 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)
throws NotStrictlyPositiveException
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
• ### 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.
• #### probability

public double probability(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 probability mass function (PMF) for the distribution. For this distribution P(X = x) always evaluates to 0.
Parameters:
x - the point at which the PMF is evaluated
Returns:
0
• #### 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
• #### 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
• #### 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()
Use this method to get information about whether the lower bound of the support is inclusive or not.
Returns:
whether the lower bound of the support is inclusive or not
• #### isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound of the support is inclusive or not.
Returns:
whether the upper bound of the support is inclusive or not
• #### 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