Extends the class GammaDist for the special case of the Erlang distribution with shape parameter \(k > 0\) and scale parameter. More...

Inheritance diagram for umontreal.ssj.probdist.ErlangDist:

Public Member Functions
	ErlangDist (int k)
	Constructs a ErlangDist object with parameters \(k\) = k and \(\lambda=1\).
	ErlangDist (int k, double lambda)
	Constructs a ErlangDist object with parameters \(k\) = k and.
int	getK ()
	Returns the parameter \(k\) for this object.
void	setParams (int k, double lambda, int d)
	Sets the parameters \(k\) and \(\lambda\) of the distribution for this object.
double[]	getParams ()
	Return a table containing parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
Public Member Functions inherited from umontreal.ssj.probdist.GammaDist
	GammaDist (double alpha)
	Constructs a GammaDist object with parameters \(\alpha\) = alpha and \(\lambda=1\).
	GammaDist (double alpha, double lambda)
	Constructs a GammaDist object with parameters \(\alpha\) = alpha and \(\lambda\) = lambda.
	GammaDist (double alpha, double lambda, int d)
	Constructs a GammaDist object with parameters \(\alpha\) = alpha and \(\lambda\) = lambda, and approximations of roughly d decimal digits of precision when computing functions.
double	density (double x)
	Returns \(f(x)\), the density evaluated at \(x\).
double	cdf (double x)
	Returns the distribution function \(F(x)\).
double	barF (double x)
	Returns the complementary distribution function.
double	inverseF (double u)
	Returns the inverse distribution function \(x = F^{-1}(u)\).
double	getMean ()
	Returns the mean.
double	getVariance ()
	Returns the variance.
double	getStandardDeviation ()
	Returns the standard deviation.
double	getAlpha ()
	Return the parameter \(\alpha\) for this object.
double	getLambda ()
	Return the parameter \(\lambda\) for this object.
Public Member Functions inherited from umontreal.ssj.probdist.ContinuousDistribution
double	inverseBrent (double a, double b, double u, double tol)
	Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method.
double	inverseBisection (double u)
	Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection.
double	getXinf ()
	Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
double	getXsup ()
	Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXinf (double xa)
	Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).
void	setXsup (double xb)
	Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\).

Static Public Member Functions
static double	density (int k, double lambda, double x)
	Computes the density function.
static double	cdf (int k, double lambda, int d, double x)
	Computes the distribution function using the gamma distribution function.
static double	barF (int k, double lambda, int d, double x)
	Computes the complementary distribution function.
static double	inverseF (int k, double lambda, int d, double u)
	Returns the inverse distribution function.
static double[]	getMLE (double[] x, int n)
	Estimates the parameters \((k,\lambda)\) of the Erlang distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).
static ErlangDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of an Erlang distribution with parameters.
static double	getMean (int k, double lambda)
	Computes and returns the mean, \(E[X] = k/\lambda\), of the Erlang distribution with parameters \(k\) and \(\lambda\).
static double	getVariance (int k, double lambda)
	Computes and returns the variance, \(\mbox{Var}[X] = k/\lambda^2\), of the Erlang distribution with parameters \(k\) and \(\lambda\).
static double	getStandardDeviation (int k, double lambda)
	Computes and returns the standard deviation of the Erlang distribution with parameters \(k\) and \(\lambda\).
Static Public Member Functions inherited from umontreal.ssj.probdist.GammaDist
static double	density (double alpha, double lambda, double x)
	Computes the density function ( `fgamma` ) at \(x\).
static double	cdf (double alpha, double lambda, int d, double x)
	Returns an approximation of the gamma distribution function with parameters \(\alpha\) = alpha and \(\lambda\) = lambda, whose density is given by ( `fgamma` ).
static double	cdf (double alpha, int d, double x)
	Equivalent to cdf (alpha, 1.0, d, x).
static double	barF (double alpha, double lambda, int d, double x)
	Computes the complementary distribution function.
static double	barF (double alpha, int d, double x)
	Same as `barF(alpha, 1.0, d, x)`.
static double	inverseF (double alpha, double lambda, int d, double u)
	Computes the inverse distribution function.
static double	inverseF (double alpha, int d, double u)
	Same as `inverseF(alpha, 1, d, u)`.
static double	getMean (double alpha, double lambda)
	Computes and returns the mean \(E[X] = \alpha/\lambda\) of the gamma distribution with parameters \(\alpha\) and \(\lambda\).
static double	getVariance (double alpha, double lambda)
	Computes and returns the variance \(\mbox{Var}[X] = \alpha/\lambda^2\) of the gamma distribution with parameters.
static double	getStandardDeviation (double alpha, double lambda)
	Computes and returns the standard deviation of the gamma distribution with parameters \(\alpha\) and \(\lambda\).

Detailed Description

Extends the class GammaDist for the special case of the Erlang distribution with shape parameter \(k > 0\) and scale parameter.

\(\lambda> 0\). This distribution is a special case of the gamma distribution for which the shape parameter \(k=\alpha\) is an integer.

Definition at line 39 of file ErlangDist.java.

Constructor & Destructor Documentation

◆ ErlangDist() [1/2]

umontreal.ssj.probdist.ErlangDist.ErlangDist ( int k )

Constructs a ErlangDist object with parameters \(k\) = k and \(\lambda=1\).

Definition at line 45 of file ErlangDist.java.

◆ ErlangDist() [2/2]

umontreal.ssj.probdist.ErlangDist.ErlangDist	(	int	k,
		double	lambda )

Constructs a ErlangDist object with parameters \(k\) = k and.

\(\lambda\) = lambda.

Definition at line 54 of file ErlangDist.java.

Member Function Documentation

◆ barF()

double umontreal.ssj.probdist.ErlangDist.barF	(	int	k,
		double	lambda,
		int	d,
		double	x )

static

Computes the complementary distribution function.

Definition at line 75 of file ErlangDist.java.

◆ cdf()

double umontreal.ssj.probdist.ErlangDist.cdf	(	int	k,
		double	lambda,
		int	d,
		double	x )

static

Computes the distribution function using the gamma distribution function.

Definition at line 68 of file ErlangDist.java.

◆ density()

double umontreal.ssj.probdist.ErlangDist.density	(	int	k,
		double	lambda,
		double	x )

static

Computes the density function.

Definition at line 61 of file ErlangDist.java.

◆ getInstanceFromMLE()

ErlangDist umontreal.ssj.probdist.ErlangDist.getInstanceFromMLE	(	double[]	x,
		int	n )

static

Creates a new instance of an Erlang distribution with parameters.

\(k\) and \(\lambda\) 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

Reimplemented from umontreal.ssj.probdist.GammaDist.

Definition at line 115 of file ErlangDist.java.

◆ getK()

int umontreal.ssj.probdist.ErlangDist.getK ( )

Returns the parameter \(k\) for this object.

Definition at line 168 of file ErlangDist.java.

◆ getMean()

double umontreal.ssj.probdist.ErlangDist.getMean	(	int	k,
		double	lambda )

static

Computes and returns the mean, \(E[X] = k/\lambda\), of the Erlang distribution with parameters \(k\) and \(\lambda\).

Returns: the mean of the Erlang distribution \(E[X] = k / \lambda\)

Definition at line 126 of file ErlangDist.java.

◆ getMLE()

double[] umontreal.ssj.probdist.ErlangDist.getMLE	(	double[]	x,
		int	n )

static

Estimates the parameters \((k,\lambda)\) 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: [ \(k\), \(\lambda\)]. The equations of the maximum likelihood are the same as for the gamma distribution. The \(k\) parameter is the rounded value of the \(\alpha\) parameter of the gamma distribution, and the \(\lambda\) parameter is equal to the

\(\beta\) parameter of the gamma distribution.

Parameters

x	the list of observations used to evaluate parameters
n	the number of observations used to evaluate parameters

Returns: returns the parameters [ \(\hat{k}\), \(\hat{\lambda}\)]

Reimplemented from umontreal.ssj.probdist.GammaDist.

Definition at line 101 of file ErlangDist.java.

◆ getParams()

double[] umontreal.ssj.probdist.ErlangDist.getParams ( )

Return a table containing parameters of the current distribution.

This table is put in regular order: [ \(k\), \(\lambda\)].

Reimplemented from umontreal.ssj.probdist.GammaDist.

Definition at line 185 of file ErlangDist.java.

◆ getStandardDeviation()

double umontreal.ssj.probdist.ErlangDist.getStandardDeviation	(	int	k,
		double	lambda )

static

Computes and returns the standard deviation of the Erlang distribution with parameters \(k\) and \(\lambda\).

Returns: the standard deviation of the Erlang distribution

Definition at line 156 of file ErlangDist.java.

◆ getVariance()

double umontreal.ssj.probdist.ErlangDist.getVariance	(	int	k,
		double	lambda )

static

Computes and returns the variance, \(\mbox{Var}[X] = k/\lambda^2\), of the Erlang distribution with parameters \(k\) and \(\lambda\).

Returns: the variance of the Erlang distribution \(\mbox{Var}[X] = k / \lambda^2\)

Definition at line 141 of file ErlangDist.java.

◆ inverseF()

double umontreal.ssj.probdist.ErlangDist.inverseF	(	int	k,
		double	lambda,
		int	d,
		double	u )

static

Returns the inverse distribution function.

Definition at line 82 of file ErlangDist.java.

◆ setParams()

void umontreal.ssj.probdist.ErlangDist.setParams	(	int	k,
		double	lambda,
		int	d )

Sets the parameters \(k\) and \(\lambda\) of the distribution for this object.

Non-static methods are computed with a rough target of d decimal digits of precision.

Definition at line 177 of file ErlangDist.java.

◆ toString()

String umontreal.ssj.probdist.ErlangDist.toString ( )

Returns a String containing information about the current distribution.

Reimplemented from umontreal.ssj.probdist.GammaDist.

Definition at line 192 of file ErlangDist.java.

The documentation for this class was generated from the following file:

src/main/java/umontreal/ssj/probdist/ErlangDist.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ ErlangDist() [1/2]

◆ ErlangDist() [2/2]

Member Function Documentation

◆ barF()

◆ cdf()

◆ density()

◆ getInstanceFromMLE()

◆ getK()

◆ getMean()

◆ getMLE()

◆ getParams()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()

◆ setParams()

◆ toString()