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:
Collaboration diagram for 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 \(\lambda\) = 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 |
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
◆ getMean()
|
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 |
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 [ \(\hat{k}\), \(\hat{\lambda}\)]
◆ getParams()
| double [] getParams | ( | ) |
Return a table containing parameters of the current distribution.
This table is put in regular order: [ \(k\), \(\lambda\)].
Implements Distribution.
◆ getStandardDeviation()
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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 |
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:
- ErlangDist.java
