umontreal.iro.lecuyer.probdist

Class ExponentialDist

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.ExponentialDist

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ExponentialDistFromMean

public class ExponentialDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the exponential distribution with mean 1/λ where λ > 0. Its density is

f (x) = λe^-λx for x >= 0,

its distribution function is

F(x) = 1 - e^-λx, for x >= 0,

and its inverse distribution function is

F^-1(u) = - ln(1 - u)/λ, for 0 < u < 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

decPrec

Constructor Summary

Constructors

Constructor and Description
ExponentialDist() Constructs an ExponentialDist object with parameter λ = 1.
ExponentialDist(double lambda) Constructs an ExponentialDist object with parameter λ = lambda.

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
static double	barF(double lambda, double x) Computes the complementary distribution function.
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(double lambda, double x) Computes the distribution function.
double	density(double x) Returns f (x), the density evaluated at x.
static double	density(double lambda, double x) Computes the density function.
static ExponentialDist	getInstanceFromMLE(double[] x, int n) Creates a new instance of an exponential distribution with parameter λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
double	getLambda() Returns the value of λ for this object.
double	getMean() Returns the mean.
static double	getMean(double lambda) Computes and returns the mean, E[X] = 1/λ, of the exponential distribution with parameter λ.
static double[]	getMLE(double[] x, int n) Estimates the parameter λ of the exponential distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
double[]	getParams() Return a table containing the parameters of the current distribution.
double	getStandardDeviation() Returns the standard deviation.
static double	getStandardDeviation(double lambda) Computes and returns the standard deviation of the exponential distribution with parameter λ.
double	getVariance() Returns the variance.
static double	getVariance(double lambda) Computes and returns the variance, Var[X] = 1/λ2, of the exponential distribution with parameter λ.
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(double lambda, double u) Computes the inverse distribution function.
void	setLambda(double lambda) Sets the value of λ for this object.
java.lang.String	toString()

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

ExponentialDist

public ExponentialDist()

Constructs an ExponentialDist object with parameter λ = 1.

ExponentialDist

public ExponentialDist(double lambda)

Constructs an ExponentialDist object with parameter λ = lambda.

Method Detail

density

public double density(double x)

Description copied from class: ContinuousDistribution

Returns f (x), the density evaluated at x.

Specified by:

density in class ContinuousDistribution

Parameters:

x - value at which the density is evaluated

Returns:

density function evaluated at x

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Parameters:

x - value at which the distribution function is evaluated

Returns:

distribution function evaluated at x

barF

public double barF(double x)

Description copied from class: ContinuousDistribution

Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:

barF in interface Distribution

Overrides:

barF in class ContinuousDistribution

Parameters:

x - value at which the complementary distribution function is evaluated

Returns:

complementary distribution function evaluated at x

inverseF

public double inverseF(double u)

Description copied from class: ContinuousDistribution

Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getMean

public double getMean()

Description copied from class: ContinuousDistribution

Returns the mean.

Specified by:

getMean in interface Distribution

Overrides:

getMean in class ContinuousDistribution

Returns:

the mean

getVariance

public double getVariance()

Description copied from class: ContinuousDistribution

Returns the variance.

Specified by:

getVariance in interface Distribution

Overrides:

getVariance in class ContinuousDistribution

Returns:

the variance

getStandardDeviation

public double getStandardDeviation()

Description copied from class: ContinuousDistribution

Returns the standard deviation.

Specified by:

getStandardDeviation in interface Distribution

Overrides:

getStandardDeviation in class ContinuousDistribution

Returns:

the standard deviation

density

public static double density(double lambda,
                             double x)

Computes the density function.

cdf

public static double cdf(double lambda,
                         double x)

Computes the distribution function.

barF

public static double barF(double lambda,
                          double x)

Computes the complementary distribution function.

inverseF

public static double inverseF(double lambda,
                              double u)

Computes the inverse distribution function.

getMLE

public static double[] getMLE(double[] x,
                              int n)

Estimates the parameter λ of the exponential distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimate is returned in a one-element array, as element 0.

Parameters:

x - the list of observations used to evaluate parameters

n - the number of observations used to evaluate parameters

Returns:

returns the parameter [ hat(λ)]

getInstanceFromMLE

public static ExponentialDist getInstanceFromMLE(double[] x,
                                                 int n)

Creates a new instance of an exponential distribution with parameter λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:

x - the list of observations to use to evaluate parameters

n - the number of observations to use to evaluate parameters

getMean

public static double getMean(double lambda)

Computes and returns the mean, E[X] = 1/λ, of the exponential distribution with parameter λ.

Returns:

the mean of the exponential distribution E[X] = 1/λ

getVariance

public static double getVariance(double lambda)

Computes and returns the variance, Var[X] = 1/λ², of the exponential distribution with parameter λ.

Returns:

the variance of the Exponential distribution Var[X] = 1/λ²

getStandardDeviation

public static double getStandardDeviation(double lambda)

Computes and returns the standard deviation of the exponential distribution with parameter λ.

Returns:

the standard deviation of the exponential distribution

getLambda

public double getLambda()

Returns the value of λ for this object.

setLambda

public void setLambda(double lambda)

Sets the value of λ for this object.

getParams

public double[] getParams()

Return a table containing the parameters of the current distribution.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object