ExponentialDist (Java Libraries for Stochastic Simulation)

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

Methods
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.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int n)` Deprecated.
`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)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - 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

Class ExponentialDist

Field Summary

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

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

ExponentialDist

ExponentialDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getLambda

setLambda

getParams

toString