SSJ
V. 2.6.

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 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
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
DiscreteDistributionInt()

Method Summary
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.

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.

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 xa of the support of the probability mass function. The probability is 0 for all x < xa.

Returns:
x lower limit of support

getXsup

public int getXsup()
Returns the upper limit xb of the support of the probability mass function. The probability is 0 for all x > xb.

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:
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 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:
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 theoritical context

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.