umontreal.ssj.probdist.GammaDistFromMoments Class Reference

Extends the GammaDist distribution with constructors accepting the mean \(\mu\) and variance \(\sigma^2\) as arguments instead of a shape parameter \(\alpha\) and a rate parameter \(\lambda\). More...

Inheritance diagram for umontreal.ssj.probdist.GammaDistFromMoments:

Public Member Functions
	GammaDistFromMoments (double mean, double var, int d)
	Constructs a gamma distribution with mean mean, variance var, and d decimal of precision.
	GammaDistFromMoments (double mean, double var)
	Constructs a gamma distribution with mean mean, and variance var.
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.
double[]	getParams ()
	Return a table containing the parameters of the current distribution.
String	toString ()
	Returns a String containing information about the current distribution.
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 \([x_a, x_b]\).

Additional Inherited Members
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[]	getMLE (double[] x, int n)
	Estimates the parameters \((\alpha,\lambda)\) of the gamma distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).
static GammaDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of a gamma distribution with parameters.
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 GammaDist distribution with constructors accepting the mean \(\mu\) and variance \(\sigma^2\) as arguments instead of a shape parameter \(\alpha\) and a rate parameter \(\lambda\).

Since

\(\mu=\alpha/ \lambda\), and \(\sigma^2=\alpha/ \lambda^2\), the shape and scale parameters are \(\alpha=\mu^2 / \sigma^2\), and \(\lambda=\mu/ \sigma^2\), respectively.

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Definition at line 40 of file GammaDistFromMoments.java.

Constructor & Destructor Documentation

GammaDistFromMoments() [1/2]

umontreal.ssj.probdist.GammaDistFromMoments.GammaDistFromMoments	(	double	mean,
		double	var,
		int	d )

Constructs a gamma distribution with mean mean, variance var, and d decimal of precision.

Parameters

mean	the desired mean.
var	the desired variance.
d	the number of decimals of precision.

Definition at line 50 of file GammaDistFromMoments.java.

GammaDistFromMoments() [2/2]

umontreal.ssj.probdist.GammaDistFromMoments.GammaDistFromMoments	(	double	mean,
		double	var )

Constructs a gamma distribution with mean mean, and variance var.

Parameters

mean	the desired mean.
var	the desired variance.

Definition at line 60 of file GammaDistFromMoments.java.

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

• src/main/java/umontreal/ssj/probdist/GammaDistFromMoments.java