Class ExponentialDistribution
java.lang.Object
org.hipparchus.distribution.continuous.AbstractRealDistribution
org.hipparchus.distribution.continuous.ExponentialDistribution
- All Implemented Interfaces:
Serializable
,RealDistribution
Implementation of the exponential distribution.
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Field Summary
Fields inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
DEFAULT_SOLVER_ABSOLUTE_ACCURACY
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Constructor Summary
ConstructorDescriptionExponentialDistribution
(double mean) Create an exponential distribution with the given mean. -
Method Summary
Modifier and TypeMethodDescriptiondouble
cumulativeProbability
(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
.double
density
(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
.double
getMean()
Access the mean.double
Use this method to get the numerical value of the mean of this distribution.double
Use this method to get the numerical value of the variance of this distribution.double
Access the lower bound of the support.double
Access the upper bound of the support.double
inverseCumulativeProbability
(double p) Computes the quantile function of this distribution.boolean
Use this method to get information about whether the support is connected, i.e.double
logDensity
(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
.Methods inherited from class org.hipparchus.distribution.continuous.AbstractRealDistribution
getSolverAbsoluteAccuracy, probability
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Constructor Details
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ExponentialDistribution
Create an exponential distribution with the given mean.- Parameters:
mean
- Mean of this distribution.- Throws:
MathIllegalArgumentException
- ifmean <= 0
.
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Method Details
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getMean
public double getMean()Access the mean.- Returns:
- the mean.
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density
public double density(double x) Returns the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. If the derivative does not exist atx
, 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
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logDensity
public double logDensity(double x) Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified pointx
. In general, the PDF is the derivative of theCDF
. If the derivative does not exist atx
, 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 ofRealDistribution.density(double)
.The default implementation simply computes the logarithm of
density(x)
.- Specified by:
logDensity
in interfaceRealDistribution
- Overrides:
logDensity
in classAbstractRealDistribution
- Parameters:
x
- the point at which the PDF is evaluated- Returns:
- the logarithm of the value of the probability density function at point
x
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cumulativeProbability
public double cumulativeProbability(double x) For a random variableX
whose values are distributed according to this distribution, this method returnsP(X <= x)
. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. The implementation of this method is based on:- Exponential Distribution, equation (1).
- 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
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inverseCumulativeProbability
Computes the quantile function of this distribution. For a random variableX
distributed according to this distribution, the returned value isinf{x in R | P(X<=x) >= p}
for0 < p <= 1
,inf{x in R | P(X<=x) > 0}
forp = 0
.
RealDistribution.getSupportLowerBound()
forp = 0
,RealDistribution.getSupportUpperBound()
forp = 1
.
0
whenp= = 0
andDouble.POSITIVE_INFINITY
whenp == 1
.- Specified by:
inverseCumulativeProbability
in interfaceRealDistribution
- Overrides:
inverseCumulativeProbability
in classAbstractRealDistribution
- Parameters:
p
- the cumulative probability- Returns:
- the smallest
p
-quantile of this distribution (largest 0-quantile forp = 0
) - Throws:
MathIllegalArgumentException
- ifp < 0
orp > 1
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getNumericalMean
public double getNumericalMean()Use this method to get the numerical value of the mean of this distribution. For mean parameterk
, the mean isk
.- Returns:
- the mean or
Double.NaN
if it is not defined
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getNumericalVariance
public double getNumericalVariance()Use this method to get the numerical value of the variance of this distribution. For mean parameterk
, the variance isk^2
.- Returns:
- the variance (possibly
Double.POSITIVE_INFINITY
as for certain cases inTDistribution
) orDouble.NaN
if it is not defined
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getSupportLowerBound
public double getSupportLowerBound()Access the lower bound of the support. This method must return the same value asinverseCumulativeProbability(0)
. In other words, this method must return
The lower bound of the support is always 0 no matter the mean parameter.inf {x in R | P(X <= x) > 0}
.- Returns:
- lower bound of the support (always 0)
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getSupportUpperBound
public double getSupportUpperBound()Access the upper bound of the support. This method must return the same value asinverseCumulativeProbability(1)
. In other words, this method must return
The upper bound of the support is always positive infinity no matter the mean parameter.inf {x in R | P(X <= x) = 1}
.- Returns:
- upper bound of the support (always Double.POSITIVE_INFINITY)
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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
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