Package jsl.utilities.distributions

Class Exponential

java.lang.Object

jsl.utilities.distributions.Distribution

jsl.utilities.distributions.Exponential

All Implemented Interfaces:

ControllableIfc, CDFIfc, ContinuousDistributionIfc, DistributionFunctionIfc, DistributionIfc, DomainIfc, FirstOrderLossFunctionIfc, InverseCDFIfc, LossFunctionDistributionIfc, MeanIfc, PDFIfc, SecondOrderLossFunctionIfc, VarianceIfc, GetNameIfc, IdentityIfc, NewInstanceIfc, ParametersIfc, GetRVariableIfc

public class Exponential
extends Distribution
implements LossFunctionDistributionIfc, ContinuousDistributionIfc, InverseCDFIfc, GetRVariableIfc

Models exponentially distributed random variables This distribution is commonly use to model the time between events

Nested Class Summary

Nested classes/interfaces inherited from class jsl.utilities.distributions.Distribution

Distribution.RandomControls

Field Summary

Fields inherited from class jsl.utilities.distributions.Distribution

myId, myName

Constructor Summary

Constructors

Constructor	Description
Exponential()	Constructs a exponential distribution with mean 1.0
Exponential(double mean)	Constructs a exponential distribution where mean is the mean of the distribution
Exponential(double[] parameters)	Constructs a exponential distributionwhere parameter[0] is the mean of the distribution
Exponential(double mean, java.lang.String name)	Constructs a exponential distribution where mean is the mean of the distribution

Method Summary

Modifier and Type	Method	Description
double	cdf(double x)	Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function
double	firstOrderLossFunction(double x)	Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]
Interval	getDomain()
double	getKurtosis()	Gets the kurtosis of the distribution
double	getMean()	Returns the mean or expected value of a distribution
double	getMoment3()
double	getMoment4()
double[]	getParameters()	Gets the parameters
RVariableIfc	getRandomVariable(RNStreamIfc rng)
double	getSkewness()	Gets the skewness of the distribution
double	getVariance()	Returns the variance of the distribution if defined
double	invCDF(double prob)	Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.
Exponential	newInstance()	Returns a new instance
double	pdf(double x)	Returns the f(x) where f represents the probability density function for the distribution.
double	secondOrderLossFunction(double x)	Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]
void	setMean(double val)	Sets the mean parameter for the distribution
void	setParameters(double[] parameters)	Sets the parameters

Methods inherited from class jsl.utilities.distributions.Distribution

getControls, getId, getName, getStandardDeviation, inverseContinuousCDFViaBisection, inverseContinuousCDFViaBisection, inverseDiscreteCDFViaSearchUp, setControls, setId, setName, toString

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface jsl.utilities.distributions.CDFIfc

cdf, complementaryCDF

Methods inherited from interface jsl.utilities.random.rvariable.GetRVariableIfc

getRandomVariable, getRandomVariable

Methods inherited from interface jsl.utilities.distributions.VarianceIfc

getStandardDeviation

Constructor Detail

Exponential

public Exponential()

Constructs a exponential distribution with mean 1.0

Exponential

public Exponential(double[] parameters)

Constructs a exponential distributionwhere parameter[0] is the mean of the distribution

Parameters:

parameters - A array containing the mean of the distribution, must be > 0.0

Exponential

public Exponential(double mean)

Constructs a exponential distribution where mean is the mean of the distribution

Parameters:

mean - The mean of the distribution, , must be > 0.0

Exponential

public Exponential(double mean,
                   java.lang.String name)

Constructs a exponential distribution where mean is the mean of the distribution

Parameters:

mean - The mean of the distribution, , must be > 0.0

name - an optional label/name

Method Detail

newInstance

public final Exponential newInstance()

Description copied from interface: NewInstanceIfc

Returns a new instance

Specified by:

newInstance in interface NewInstanceIfc

Specified by:

newInstance in class Distribution

Returns:

the new instance

getDomain

public final Interval getDomain()

Specified by:

getDomain in interface DomainIfc

setMean

public final void setMean(double val)

Sets the mean parameter for the distribution

Parameters:

val - The mean of the distribution, must be > 0.0

getMean

public final double getMean()

Description copied from interface: MeanIfc

Returns the mean or expected value of a distribution

Specified by:

getMean in interface MeanIfc

Returns:

double the mean or expected value for the distribution

getMoment3

public final double getMoment3()

getMoment4

public final double getMoment4()

cdf

public final double cdf(double x)

Description copied from interface: CDFIfc

Returns the F(x) = Pr{X <= x} where F represents the cumulative distribution function

Specified by:

cdf in interface CDFIfc

Parameters:

x - a double representing the upper limit

Returns:

a double representing the probability

invCDF

public final double invCDF(double prob)

Description copied from interface: InverseCDFIfc

Provides the inverse cumulative distribution function for the distribution While closed form solutions for the inverse cdf may not exist, numerical search methods can be used to solve F(X) = U.

Specified by:

invCDF in interface InverseCDFIfc

Parameters:

prob - The probability to be evaluated for the inverse, p must be [0,1] or an IllegalArgumentException is thrown

Returns:

The inverse cdf evaluated at the supplied probability

pdf

public final double pdf(double x)

Description copied from interface: PDFIfc

Returns the f(x) where f represents the probability density function for the distribution. Note this is not a probability.

Specified by:

pdf in interface PDFIfc

Parameters:

x - a double representing the value to be evaluated

Returns:

f(x)

getVariance

public final double getVariance()

Description copied from interface: VarianceIfc

Returns the variance of the distribution if defined

Specified by:

getVariance in interface VarianceIfc

Returns:

double the variance of the random variable

getKurtosis

public final double getKurtosis()

Gets the kurtosis of the distribution

Returns:

the kurtosis

getSkewness

public final double getSkewness()

Gets the skewness of the distribution

Returns:

the skewness

setParameters

public final void setParameters(double[] parameters)

Description copied from interface: ParametersIfc

Sets the parameters

Specified by:

setParameters in interface ParametersIfc

Parameters:

parameters - an array of doubles representing the parameters

getParameters

public final double[] getParameters()

Description copied from interface: ParametersIfc

Gets the parameters

Specified by:

getParameters in interface ParametersIfc

Returns:

Returns an array of the parameters

getRandomVariable

public final RVariableIfc getRandomVariable(RNStreamIfc rng)

Specified by:

getRandomVariable in interface GetRVariableIfc

Overrides:

getRandomVariable in class Distribution

Parameters:

rng - the stream to use

Returns:

a random variable

firstOrderLossFunction

public double firstOrderLossFunction(double x)

Description copied from interface: FirstOrderLossFunctionIfc

Computes the first order loss function for the function for given value of x, G1(x) = E[max(X-x,0)]

Specified by:

firstOrderLossFunction in interface FirstOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, E[max(X-x,0)]

secondOrderLossFunction

public double secondOrderLossFunction(double x)

Description copied from interface: SecondOrderLossFunctionIfc

Computes the 2nd order loss function for the distribution function for given value of x, G2(x) = (1/2)E[max(X-x,0)*max(X-x-1,0)]

Specified by:

secondOrderLossFunction in interface SecondOrderLossFunctionIfc

Parameters:

x - The value to be evaluated

Returns:

The loss function value, (1/2)E[max(X-x,0)*max(X-x-1,0)]