Extends the class ContinuousDistribution for the exponential distribution [99] (page 494) with mean \(1/\lambda\) where \(\lambda> 0\). More...

Inheritance diagram for ExponentialDist:

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Collaboration diagram for ExponentialDist:

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Public Member Functions
	ExponentialDist ()
	Constructs an `ExponentialDist` object with parameter \(\lambda\) = 1.

	ExponentialDist (double lambda)
	Constructs an `ExponentialDist` object with parameter \(\lambda\) = `lambda`.

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	getLambda ()
	Returns the value of \(\lambda\) for this object.

void	setLambda (double lambda)
	Sets the value of \(\lambda\) 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 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 (double lambda, double x)
	Computes the density function.

static double	cdf (double lambda, double x)
	Computes the distribution function.

static double	barF (double lambda, double x)
	Computes the complementary distribution function.

static double	inverseF (double lambda, double u)
	Computes the inverse distribution function.

static double []	getMLE (double[] x, int n)
	Estimates the parameter \(\lambda\) of the exponential distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\). More...

static ExponentialDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of an exponential distribution with parameter \(\lambda\) estimated using the maximum likelihood method based on the \(n\) observations \(x[i]\), \(i = 0, 1, …, n-1\). More...

static double	getMean (double lambda)
	Computes and returns the mean, \(E[X] = 1/\lambda\), of the exponential distribution with parameter \(\lambda\). More...

static double	getVariance (double lambda)
	Computes and returns the variance, \(\mbox{Var}[X] = 1/\lambda^2\), of the exponential distribution with parameter \(\lambda\). More...

static double	getStandardDeviation (double lambda)
	Computes and returns the standard deviation of the exponential distribution with parameter \(\lambda\). 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

Detailed Description

Extends the class ContinuousDistribution for the exponential distribution [99] (page 494) with mean \(1/\lambda\) where \(\lambda> 0\).

Its density is

\[ f(x) = \lambda e^{-\lambda x} \qquad\mbox{for }x\ge0, \tag{fexpon} \]

its distribution function is

\[ F(x) = 1 - e^{-\lambda x},\qquad\mbox{for }x \ge0, \tag{Fexpon} \]

and its inverse distribution function is

\[ F^{-1}(u) = -\ln(1-u)/\lambda, \qquad\mbox{for } 0 < u < 1. \]

Member Function Documentation

◆ barF()

double barF ( double x )

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Implements Distribution.

◆ cdf()

double cdf ( double x )

Returns the distribution function \(F(x)\).

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Implements Distribution.

◆ getInstanceFromMLE()

static ExponentialDist getInstanceFromMLE	(	double []	x,
		int	n
	)

static

Creates a new instance of an exponential distribution with parameter \(\lambda\) 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 double getMean ( double lambda )

static

Computes and returns the mean, \(E[X] = 1/\lambda\), of the exponential distribution with parameter \(\lambda\).

Returns: the mean of the exponential distribution \(E[X] = 1 / \lambda\)

◆ getMLE()

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

static

Estimates the parameter \(\lambda\) of the exponential distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).

The estimate is returned in a one-element array, as element 0. The equation of the maximum likelihood is defined as \(\hat{\lambda} = 1/\bar{x}_n\), where \(\bar{x}_n\) is the average of \(x[0],…,x[n-1]\) (see [99] (page 506)).

Parameters

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

Returns: returns the parameter [ \(\hat{\lambda}\)]

◆ getStandardDeviation()

static double getStandardDeviation ( double lambda )

static

Computes and returns the standard deviation of the exponential distribution with parameter \(\lambda\).

Returns: the standard deviation of the exponential distribution

◆ getVariance()

static double getVariance ( double lambda )

static

Computes and returns the variance, \(\mbox{Var}[X] = 1/\lambda^2\), of the exponential distribution with parameter \(\lambda\).

Returns: the variance of the Exponential distribution \(\mbox{Var}[X] = 1 / \lambda^2\)

◆ inverseF()

double inverseF ( double u )

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters

u	value in the interval \((0,1)\) for which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Implements Distribution.

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

ExponentialDist.java

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ barF()

◆ cdf()

◆ getInstanceFromMLE()

◆ getMean()

◆ getMLE()

◆ getStandardDeviation()

◆ getVariance()

◆ inverseF()