SSJ  3.3.1
Stochastic Simulation in Java
Public Member Functions | Static Public Member Functions | List of all members
ErlangDist Class Reference

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

Inheritance diagram for ErlangDist:
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Collaboration diagram for ErlangDist:
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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 \(\lambda\) = lambda.
 
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. More...
 
double [] getParams ()
 Return a table containing parameters of the current distribution. More...
 
String toString ()
 Returns a String containing information about the current distribution.
 
- Public Member Functions inherited from 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)
 
double cdf (double x)
 Returns the distribution function \(F(x)\). More...
 
double barF (double x)
 Returns \(\bar{F}(x) = 1 - F(x)\). More...
 
double inverseF (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...
 
double getMean ()
 Returns the mean of the distribution function.
 
double getVariance ()
 Returns the variance of the distribution function.
 
double getStandardDeviation ()
 Returns the standard deviation of the distribution function.
 
double getAlpha ()
 Return the parameter \(\alpha\) for this object.
 
double getLambda ()
 Return the parameter \(\lambda\) for this object.
 
void setParams (double alpha, double lambda, int d)
 
double [] getParams ()
 Return a table containing the parameters of the current distribution. More...
 
String toString ()
 Returns a String containing information about the current distribution.
 
- Public Member Functions inherited from ContinuousDistribution
abstract double density (double x)
 Returns \(f(x)\), the density evaluated at \(x\). More...
 
double barF (double x)
 Returns the complementary distribution function. More...
 
double inverseBrent (double a, double b, double u, double tol)
 Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...
 
double inverseBisection (double u)
 Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(x = F^{-1}(u)\). More...
 
double getMean ()
 Returns the mean. More...
 
double getVariance ()
 Returns the variance. More...
 
double getStandardDeviation ()
 Returns the standard deviation. More...
 
double getXinf ()
 Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
double getXsup ()
 Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXinf (double xa)
 Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXsup (double xb)
 Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 

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 \(x[i]\), \(i = 0, 1,…, n-1\). More...
 
static ErlangDist getInstanceFromMLE (double[] x, int n)
 Creates a new instance of an Erlang distribution with parameters \(k\) and \(\lambda\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...
 
static double getMean (int k, double lambda)
 Computes and returns the mean, \(E[X] = k/\lambda\), of the Erlang distribution with parameters \(k\) and \(\lambda\). More...
 
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 \(\lambda\). More...
 
static double getStandardDeviation (int k, double lambda)
 Computes and returns the standard deviation of the Erlang distribution with parameters \(k\) and \(\lambda\). More...
 
- Static Public Member Functions inherited from 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 ). More...
 
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 [] getMLE (double[] x, int n)
 Estimates the parameters \((\alpha,\lambda)\) of the gamma distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\). More...
 
static GammaDist getInstanceFromMLE (double[] x, int n)
 Creates a new instance of a gamma distribution with parameters \(\alpha\) and \(\lambda\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...
 
static double getMean (double alpha, double lambda)
 Computes and returns the mean \(E[X] = \alpha/\lambda\) of the gamma distribution with parameters \(\alpha\) and \(\lambda\). More...
 
static double getVariance (double alpha, double lambda)
 Computes and returns the variance \(\mbox{Var}[X] = \alpha/\lambda^2\) of the gamma distribution with parameters \(\alpha\) and \(\lambda\). More...
 
static double getStandardDeviation (double alpha, double lambda)
 Computes and returns the standard deviation of the gamma distribution with parameters \(\alpha\) and \(\lambda\). More...
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 
- Static Package Functions inherited from GammaDist
static double mybelog (double x)
 

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.

Member Function Documentation

◆ getInstanceFromMLE()

static 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
xthe list of observations to use to evaluate parameters
nthe number of observations to use to evaluate parameters

◆ getMean()

static double 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 \(E[X] = k / \lambda\)

◆ getMLE()

static double [] 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
xthe list of observations used to evaluate parameters
nthe number of observations used to evaluate parameters
Returns
returns the parameters [ \(\hat{k}\), \(\hat{\lambda}\)]

◆ getParams()

double [] getParams ( )

Return a table containing parameters of the current distribution.

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

Implements Distribution.

◆ getStandardDeviation()

static double 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

◆ getVariance()

static double 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 \(\mbox{Var}[X] = k / \lambda^2\)

◆ setParams()

void 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.


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