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java.lang.Objectorg.apache.commons.math3.distribution.AbstractRealDistribution
org.apache.commons.math3.distribution.WeibullDistribution
public class WeibullDistribution
Implementation of the Weibull distribution. This implementation uses the two parameter form of the distribution defined by Weibull Distribution, equations (1) and (2).
Field Summary | |
---|---|
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 | |
---|---|
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,
double inverseCumAccuracy)
Creates a Weibull distribution. |
Method Summary | |
---|---|
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. |
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 |
---|
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
private static final long serialVersionUID
private final double shape
private final double scale
private final double solverAbsoluteAccuracy
private double numericalMean
private boolean numericalMeanIsCalculated
private double numericalVariance
private boolean numericalVarianceIsCalculated
Constructor Detail |
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public WeibullDistribution(double alpha, double beta) throws NotStrictlyPositiveException
alpha
- Shape parameter.beta
- Scale parameter.
NotStrictlyPositiveException
- if alpha <= 0
or
beta <= 0
.public WeibullDistribution(double alpha, double beta, double inverseCumAccuracy)
alpha
- Shape parameter.beta
- Scale parameter.inverseCumAccuracy
- Maximum absolute error in inverse
cumulative probability estimates
(defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).
NotStrictlyPositiveException
- if alpha <= 0
or
beta <= 0
.public WeibullDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy) throws NotStrictlyPositiveException
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
).
NotStrictlyPositiveException
- if alpha <= 0
or
beta <= 0
.Method Detail |
---|
public double getShape()
alpha
.
alpha
.public double getScale()
beta
.
beta
.public double density(double x)
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.
x
- the point at which the PDF is evaluated
x
public double cumulativeProbability(double x)
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.
x
- the point at which the CDF is evaluated
x
public double inverseCumulativeProbability(double p)
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
.RealDistribution.getSupportLowerBound()
for p = 0
,RealDistribution.getSupportUpperBound()
for p = 1
.0
when p == 0
and
Double.POSITIVE_INFINITY
when p == 1
.
inverseCumulativeProbability
in interface RealDistribution
inverseCumulativeProbability
in class AbstractRealDistribution
p
- the cumulative probability
p
-quantile of this distribution
(largest 0-quantile for p = 0
)protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public double getNumericalMean()
scale * Gamma(1 + (1 / shape))
, where Gamma()
is the Gamma-function.
Double.NaN
if it is not definedprotected double calculateNumericalMean()
getNumericalMean()
public double getNumericalVariance()
scale^2 * Gamma(1 + (2 / shape)) - mean^2
where Gamma()
is the Gamma-function.
Double.POSITIVE_INFINITY
as
for certain cases in TDistribution
) or Double.NaN
if it
is not definedprotected double calculateNumericalVariance()
getNumericalVariance()
public double getSupportLowerBound()
inverseCumulativeProbability(0)
. In other words, this
method must return
inf {x in R | P(X <= x) > 0}
.
public double getSupportUpperBound()
inverseCumulativeProbability(1)
. In other words, this
method must return
inf {x in R | P(X <= x) = 1}
.
Double.POSITIVE_INFINITY
)public boolean isSupportLowerBoundInclusive()
getSupporLowerBound()
is finite and
density(getSupportLowerBound())
returns a non-NaN, non-infinite
value.
public boolean isSupportUpperBoundInclusive()
getSupportUpperBound()
is finite and
density(getSupportUpperBound())
returns a non-NaN, non-infinite
value.
public boolean isSupportConnected()
true
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