DiscreteDistribution Class Reference

This class implements discrete distributions over a finite set of real numbers (also over integers as a particular case). More...

Inheritance diagram for DiscreteDistribution:

Collaboration diagram for DiscreteDistribution:

Public Member Functions
	DiscreteDistribution (double[] values, double[] prob, int n)
	Constructs a discrete distribution over the \(n\) values contained in array values, with probabilities given in array prob. More...
	DiscreteDistribution (int[] values, double[] prob, int n)
	Similar to DiscreteDistribution(double[], double[], int).
double	cdf (double x)
double	barF (double x)
double	inverseF (double u)
double	getMean ()
	Computes the mean \(E[X] = \sum_i^{} p_i x_i\) of the distribution.
double	getVariance ()
	Computes the variance \(\mbox{Var}[X] = \sum_i^{} p_i (x_i - E[X])^2\) of the distribution.
double	getStandardDeviation ()
	Computes the standard deviation of the distribution.
double []	getParams ()
	Returns a table containing the parameters of the current distribution. More...
int	getN ()
	Returns the number of possible values \(x_i\).
double	prob (int i)
	Returns \(p_i\), the probability of the \(i\)-th value, for. More...
double	getValue (int i)
	Returns the \(i\)-th value \(x_i\), for \(0\le i<n\).
double	getXinf ()
	Returns the lower limit \(x_0\) of the support of the distribution. More...
double	getXsup ()
	Returns the upper limit \(x_{n-1}\) of the support of the distribution. More...
String	toString ()
	Returns a String containing information about the current distribution.

Protected Attributes
double	cdf [] = null
double	pr [] = null
int	xmin = 0
int	xmax = 0
int	xmed = 0
int	nVal
double	sortedVal []
double	supportA = Double.NEGATIVE_INFINITY
double	supportB = Double.POSITIVE_INFINITY

Detailed Description

This class implements discrete distributions over a finite set of real numbers (also over integers as a particular case).

We assume that the random variable \(X\) of interest can take one of the \(n\) values

\(x_0 < \cdots< x_{n-1}\), which must be sorted by increasing order. \(X\) can take the value \(x_k\) with probability \(p_k = P[X = x_k]\). In addition to the methods specified in the interface umontreal.ssj.probdist.Distribution, a method that returns the probability \(p_k\) is supplied.

Constructor & Destructor Documentation

DiscreteDistribution()

DiscreteDistribution	(	double []	values,
		double []	prob,
		int	n
	)

Constructs a discrete distribution over the \(n\) values contained in array values, with probabilities given in array prob.

Both arrays must have at least \(n\) elements, the probabilities must sum to 1, and the values are assumed to be sorted by increasing order.

Member Function Documentation

barF()

double barF

(

double

x

)

Parameters

x	value at which the complementary distribution function is evaluated

Returns

the complementary distribution function evaluated at x

Implements Distribution.

cdf()

double cdf

(

double

x

)

Parameters

x	value at which the cdf is evaluated

Returns

the cdf evaluated at x

Implements Distribution.

getParams()

double [] getParams

(

)

Returns a table containing the parameters of the current distribution.

This table is built in regular order, according to constructor DiscreteDistribution(double[] params) order.

Implements Distribution.

getXinf()

double getXinf

(

)

Returns the lower limit \(x_0\) of the support of the distribution.

Returns

\(x\) lower limit of support

getXsup()

double getXsup

(

)

Returns the upper limit \(x_{n-1}\) of the support of the distribution.

Returns

\(x\) upper limit of support

inverseF()

double inverseF

(

double

u

)

Parameters

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

Returns

the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException	if \(u\) is not in the interval \((0,1)\)
ArithmeticException	if the inverse cannot be computed, for example if it would give infinity in a theoretical context

Implements Distribution.

prob()

double prob

(

int

i

)

Returns \(p_i\), the probability of the \(i\)-th value, for.

\(0\le i<n\).

Parameters

i	value number, \(0\le i < n\)

Returns

the probability of value i

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

• DiscreteDistribution.java