umontreal.iro.lecuyer.probdist
Class ErlangDist

java.lang.Object
  umontreal.iro.lecuyer.probdist.ContinuousDistribution
      umontreal.iro.lecuyer.probdist.GammaDist
          umontreal.iro.lecuyer.probdist.ErlangDist

All Implemented Interfaces:

Distribution

public class ErlangDist
extends GammaDist

Extends the class GammaDist for the special case of the Erlang distribution with shape parameter k > 0 and scale parameter λ > 0. This distribution is a special case of the gamma distribution for which the shape parameter k = α is an integer.

Field Summary

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

decPrec

Constructor Summary

ErlangDist(int k)
Constructs a ErlangDist object with parameters k = k and λ = 1.

ErlangDist(int k, double lambda)
Constructs a ErlangDist object with parameters k = k and λ = lambda.

Method Summary

static double	barF(int k, double lambda, int d, double x) Computes the complementary distribution function.
static double	cdf(int k, double lambda, int d, double x) Computes the distribution function using the gamma distribution function.
static double	density(int k, double lambda, double x) Computes the density function.
static ErlangDist	getInstanceFromMLE(double[] x, int n) Creates a new instance of an Erlang distribution with parameters k and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
int	getK() Returns the parameter k for this object.
static double	getMean(int k, double lambda) Computes and returns the mean, E[X] = k/λ, of the Erlang distribution with parameters k and λ.
static double[]	getMLE(double[] x, int n) Estimates the parameters (k, λ) of the Erlang distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
double[]	getParams() Return a table containing parameters of the current distribution.
static double	getStandardDeviation(int k, double lambda) Computes and returns the standard deviation of the Erlang distribution with parameters k and λ.
static double	getVariance(int k, double lambda) Computes and returns the variance, Var[X] = k/λ2, of the Erlang distribution with parameters k and λ.
static double	inverseF(int k, double lambda, int d, double u) Returns the inverse distribution function.
void	setParams(int k, double lambda, int d) Sets the parameters k and λ of the distribution for this object.
String	toString()

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

barF, barF, barF, cdf, cdf, cdf, density, density, getAlpha, getLambda, getMean, getMean, getStandardDeviation, getStandardDeviation, getVariance, getVariance, inverseF, inverseF, inverseF, setParams

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

ErlangDist

public ErlangDist(int k)

Constructs a ErlangDist object with parameters k = k and λ = 1.

ErlangDist

public ErlangDist(int k,
                  double lambda)

Constructs a ErlangDist object with parameters k = k and λ = lambda.

Method Detail

density

public static double density(int k,
                             double lambda,
                             double x)

Computes the density function.

cdf

public static double cdf(int k,
                         double lambda,
                         int d,
                         double x)

Computes the distribution function using the gamma distribution function.

barF

public static double barF(int k,
                          double lambda,
                          int d,
                          double x)

Computes the complementary distribution function.

inverseF

public static double inverseF(int k,
                              double lambda,
                              int d,
                              double u)

Returns the inverse distribution function.

getMLE

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

Estimates the parameters (k, λ) of the Erlang distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [k, λ].

Parameters:

x - the list of observations used to evaluate parameters

n - the number of observations used to evaluate parameters

Returns:

returns the parameters [hat(k), hat(λ)]

getInstanceFromMLE

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

Creates a new instance of an Erlang distribution with parameters k and 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(int k,
                             double lambda)

Computes and returns the mean, E[X] = k/λ, of the Erlang distribution with parameters k and λ.

Returns:

the mean of the Erlang distribution E[X] = k/λ

getVariance

public static double getVariance(int k,
                                 double lambda)

Computes and returns the variance, Var[X] = k/λ², of the Erlang distribution with parameters k and λ.

Returns:

the variance of the Erlang distribution Var[X] = k/λ²

getStandardDeviation

public static double getStandardDeviation(int k,
                                          double lambda)

Computes and returns the standard deviation of the Erlang distribution with parameters k and λ.

Returns:

the standard deviation of the Erlang distribution

getK

public int getK()

Returns the parameter k for this object.

setParams

public void setParams(int k,
                      double lambda,
                      int d)

Sets the parameters k and λ of the distribution for this object. Non-static methods are computed with a rough target of d decimal digits of precision.

getParams

public double[] getParams()

Return a table containing parameters of the current distribution. This table is put in regular order: [k, λ].

Specified by:

getParams in interface Distribution

Overrides:

getParams in class GammaDist

toString

public String toString()

Overrides:

toString in class GammaDist