org.apache.commons.math3.distribution
Class ExponentialDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.AbstractRealDistribution
      extended by org.apache.commons.math3.distribution.ExponentialDistribution
All Implemented Interfaces:
Serializable, RealDistribution

public class ExponentialDistribution
extends AbstractRealDistribution

Implementation of the exponential distribution.

Version:
$Id: ExponentialDistribution.java 1416643 2012-12-03 19:37:14Z tn $
See Also:
Exponential distribution (Wikipedia), Exponential distribution (MathWorld), Serialized Form

Field Summary
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
          Default inverse cumulative probability accuracy.
 
Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
 
Constructor Summary
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, double inverseCumAccuracy)
          Creates an exponential distribution.
 
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()
          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 sample()
          Generate a random value sampled from this distribution.
 
Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
cumulativeProbability, probability, probability, reseedRandomGenerator, sample
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.

Since:
2.1
See Also:
Constant Field Values
Constructor Detail

ExponentialDistribution

public ExponentialDistribution(double mean)
Create an exponential distribution with the given mean.

Parameters:
mean - mean of this distribution.

ExponentialDistribution

public ExponentialDistribution(double mean,
                               double inverseCumAccuracy)
Create an exponential distribution with the given mean.

Parameters:
mean - Mean of this distribution.
inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NotStrictlyPositiveException - if mean <= 0.
Since:
2.1

ExponentialDistribution

public ExponentialDistribution(RandomGenerator rng,
                               double mean,
                               double inverseCumAccuracy)
                        throws NotStrictlyPositiveException
Creates an exponential distribution.

Parameters:
rng - Random number generator.
mean - Mean of this distribution.
inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NotStrictlyPositiveException - if mean <= 0.
Since:
3.1
Method Detail

getMean

public double getMean()
Access the mean.

Returns:
the mean.

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. The implementation of this method is based on:

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

inverseCumulativeProbability

public double inverseCumulativeProbability(double p)
                                    throws OutOfRangeException
Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is The default implementation returns Returns 0 when p= = 0 and Double.POSITIVE_INFINITY when p == 1.

Specified by:
inverseCumulativeProbability in interface RealDistribution
Overrides:
inverseCumulativeProbability in class AbstractRealDistribution
Parameters:
p - the cumulative probability
Returns:
the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
Throws:
OutOfRangeException - if p < 0 or p > 1

sample

public double sample()
Generate a random value sampled from this distribution. The default implementation uses the inversion method.

Algorithm Description: this implementation uses the Inversion Method to generate exponentially distributed random values from uniform deviates.

Specified by:
sample in interface RealDistribution
Overrides:
sample in class AbstractRealDistribution
Returns:
a random value.
Since:
2.2

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:
getSolverAbsoluteAccuracy in class AbstractRealDistribution
Returns:
the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution. For mean parameter k, the mean is k.

Returns:
the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution. For mean parameter k, the variance is k^2.

Returns:
the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

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 mean parameter.

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 mean parameter.

Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()
Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:
true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:
true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

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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