umontreal.iro.lecuyer.probdist

Class DiscreteDistributionInt

java.lang.Object

umontreal.iro.lecuyer.probdist.DiscreteDistributionInt

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

BernoulliDist, BinomialDist, GeometricDist, HypergeometricDist, LogarithmicDist, NegativeBinomialDist, PoissonDist, UniformIntDist

public abstract class DiscreteDistributionInt
extends java.lang.Object
implements Distribution

Classes implementing discrete distributions over the integers should inherit from this class. It specifies the signatures of methods for computing the mass function (or probability) p(x) = P[X = x], distribution function F(x), complementary distribution function bar(F)(x), and inverse distribution function F^-1(u), for a random variable X with a discrete distribution over the integers.

WARNING: the complementary distribution function is defined as bar(F)(j) = P[X >= j] (for integers j, so that for discrete distributions in SSJ, F(j) + bar(F)(j)≠1 since both include the term P[X = j].

The implementing classes provide both static and non-static methods to compute the above functions. The non-static methods require the creation of an object of class DiscreteDistributionInt; all the non-negligible terms of the mass and distribution functions will be precomputed by the constructor and kept in arrays. Subsequent accesses will be very fast. The static methods do not require the construction of an object. These static methods are not specified in this abstract class because the number and types of their parameters depend on the distribution. When methods have to be called several times with the same parameters for the distributions, it is usually more efficient to create an object and use its non-static methods instead of the static ones. This trades memory for speed.

Field Summary

Fields

Modifier and Type	Field and Description
static double	EPSILON Environment variable that determines what probability terms can be considered as negligible when building precomputed tables for distribution and mass functions.

Constructor Summary

Constructors

Constructor and Description
DiscreteDistributionInt()

Method Summary

Modifier and Type	Method and Description
double	barF(double x) Returns bar(F)(x), the complementary distribution function.
double	barF(int x) Returns bar(F)(x), the complementary distribution function.
double	cdf(double x) Returns the distribution function F evaluated at x (see).
abstract double	cdf(int x) Returns the distribution function F evaluated at x (see).
int	getXinf() Returns the lower limit xa of the support of the probability mass function.
int	getXsup() Returns the upper limit xb of the support of the probability mass function.
double	inverseF(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
int	inverseFInt(double u) Returns the inverse distribution function F-1(u), where 0 <= u <= 1.
abstract double	prob(int x) Returns p(x), the probability of x, which should be a real number in the interval [0, 1].

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface umontreal.iro.lecuyer.probdist.Distribution

getMean, getParams, getStandardDeviation, getVariance

Field Detail

EPSILON

public static double EPSILON

Environment variable that determines what probability terms can be considered as negligible when building precomputed tables for distribution and mass functions. Probabilities smaller than EPSILON are not stored in the DiscreteDistribution objects (such as those of class PoissonDist, etc.), but are computed directly each time they are needed (which should be very seldom). The default value is set to 10^-16.

Constructor Detail

DiscreteDistributionInt

public DiscreteDistributionInt()

Method Detail

prob

public abstract double prob(int x)

Returns p(x), the probability of x, which should be a real number in the interval [0, 1].

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

cdf

public double cdf(double x)

Returns the distribution function F evaluated at x (see). Calls the cdf(int) method.

Specified by:

cdf in interface Distribution

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the distribution function evaluated at x

cdf

public abstract double cdf(int x)

Returns the distribution function F evaluated at x (see).

Parameters:

x - value at which the distribution function must be evaluated

Returns:

the distribution function evaluated at x

barF

public double barF(double x)

Returns bar(F)(x), the complementary distribution function. Calls the barF(int) method.

Specified by:

barF in interface Distribution

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x

barF

public double barF(int x)

Returns bar(F)(x), the complementary distribution function. See the WARNING above.

Parameters:

x - value at which the complementary distribution function must be evaluated

Returns:

the complementary distribution function evaluated at x

getXinf

public int getXinf()

Returns the lower limit x_a of the support of the probability mass function. The probability is 0 for all x < x_a.

Returns:

x lower limit of support

getXsup

public int getXsup()

Returns the upper limit x_b of the support of the probability mass function. The probability is 0 for all x > x_b.

Returns:

x upper limit of support

inverseF

public double inverseF(double u)

Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. Calls the inverseFInt method.

Specified by:

inverseF in interface Distribution

Parameters:

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

Returns:

the inverse distribution function evaluated at u

Throws:

java.lang.IllegalArgumentException - if u is not in the interval (0, 1)

java.lang.ArithmeticException - if the inverse cannot be computed, for example if it would give infinity in a theoritical context

inverseFInt

public int inverseFInt(double u)

Returns the inverse distribution function F^-1(u), where 0 <= u <= 1. The default implementation uses binary search.

Parameters:

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

Returns:

the inverse distribution function evaluated at u

Throws:

java.lang.IllegalArgumentException - if u is not in the interval (0, 1)

java.lang.ArithmeticException - if the inverse cannot be computed, for example if it would give infinity in a theoritical context