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java.lang.Objectorg.apache.commons.math3.distribution.AbstractRealDistribution
org.apache.commons.math3.distribution.ExponentialDistribution
public class ExponentialDistribution
Implementation of the exponential distribution.
Field Summary | |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy. |
private double |
mean
The mean of this distribution. |
private static long |
serialVersionUID
Serializable version identifier |
private double |
solverAbsoluteAccuracy
Inverse cumulative probability accuracy. |
Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution |
---|
randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY |
Constructor Summary | |
---|---|
ExponentialDistribution(double mean)
Create a exponential distribution with the given mean. |
|
ExponentialDistribution(double mean,
double inverseCumAccuracy)
Create a exponential distribution with the given mean. |
Method Summary | |
---|---|
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 |
getMean()
Access the mean. |
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. |
protected double |
getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation. |
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()
Use this method to get information about whether the lower bound of the support is inclusive or not. |
boolean |
isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound of the support is inclusive or not. |
double |
probability(double x)
For a random variable X whose values are distributed according
to this distribution, this method returns P(X = x) . |
double |
sample()
Generate a random value sampled from this distribution. |
Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution |
---|
cumulativeProbability, reseedRandomGenerator, 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 mean
private final double solverAbsoluteAccuracy
Constructor Detail |
---|
public ExponentialDistribution(double mean)
mean
- mean of this distribution.public ExponentialDistribution(double mean, double inverseCumAccuracy) throws NotStrictlyPositiveException
mean
- Mean of this distribution.inverseCumAccuracy
- Maximum absolute error in inverse
cumulative probability estimates (defaults to
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).
NotStrictlyPositiveException
- if mean <= 0
.Method Detail |
---|
public double getMean()
public double probability(double x)
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.
x
- the point at which the PMF is evaluated
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.
The implementation of this method is based on:
x
- the point at which the CDF is evaluated
x
public double inverseCumulativeProbability(double p) throws OutOfRangeException
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
)
OutOfRangeException
- if p < 0
or p > 1
public double sample()
Algorithm Description: this implementation uses the Inversion Method to generate exponentially distributed random values from uniform deviates.
sample
in interface RealDistribution
sample
in class AbstractRealDistribution
protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public double getNumericalMean()
k
, the mean is k
.
Double.NaN
if it is not definedpublic double getNumericalVariance()
k
, the variance is k^2
.
Double.POSITIVE_INFINITY
as
for certain cases in TDistribution
) or Double.NaN
if it
is not definedpublic 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}
.
public boolean isSupportLowerBoundInclusive()
public boolean isSupportUpperBoundInclusive()
public boolean isSupportConnected()
true
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