public class ExponentialDistribution extends AbstractRealDistribution
Modifier and Type | Field and Description |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
|
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description |
---|
ExponentialDistribution(double mean)
Create an exponential distribution with the given mean.
|
ExponentialDistribution(double mean,
double inverseCumAccuracy)
Create an exponential distribution with the given mean.
|
ExponentialDistribution(RandomGenerator rng,
double mean)
Creates an exponential distribution.
|
ExponentialDistribution(RandomGenerator rng,
double mean,
double inverseCumAccuracy)
Creates an exponential distribution.
|
Modifier and Type | Method and Description |
---|---|
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()
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 . |
double |
sample()
Generate a random value sampled from this distribution.
|
cumulativeProbability, probability, probability, reseedRandomGenerator, sample
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
public ExponentialDistribution(double mean)
Note: this constructor will implicitly create an instance of
Well19937c
as random generator to be used for sampling only (see
sample()
and AbstractRealDistribution.sample(int)
). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
mean
- mean of this distribution.public ExponentialDistribution(double mean, double inverseCumAccuracy)
Note: this constructor will implicitly create an instance of
Well19937c
as random generator to be used for sampling only (see
sample()
and AbstractRealDistribution.sample(int)
). In case no sampling is
needed for the created distribution, it is advised to pass null
as random generator via the appropriate constructors to avoid the
additional initialisation overhead.
mean
- Mean of this distribution.inverseCumAccuracy
- Maximum absolute error in inverse
cumulative probability estimates (defaults to
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if mean <= 0
.public ExponentialDistribution(RandomGenerator rng, double mean) throws NotStrictlyPositiveException
rng
- Random number generator.mean
- Mean of this distribution.NotStrictlyPositiveException
- if mean <= 0
.public ExponentialDistribution(RandomGenerator rng, double mean, double inverseCumAccuracy) throws NotStrictlyPositiveException
rng
- Random number generator.mean
- Mean of this distribution.inverseCumAccuracy
- Maximum absolute error in inverse
cumulative probability estimates (defaults to
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if mean <= 0
.public double getMean()
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 evaluatedx
public double logDensity(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. 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)
.logDensity
in class AbstractRealDistribution
x
- the point at which the PDF is evaluatedx
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 evaluatedx
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 probabilityp
-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()
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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