Package umontreal.iro.lecuyer.probdistmulti

This package contains Java classes providing methods to compute mass, density, distribution and complementary distribution functions for some multi-dimensional discrete and continuous probability distributions.

See:
Description

Class Summary

BiNormalDist	Extends the class ContinuousDistribution2Dim for the bivariate normal distribution.
BiNormalDonnellyDist	Extends the class BiNormalDist for the bivariate normal distribution using a translation of Donnelly's FORTRAN code.
BiNormalGenzDist	Extends the class BiNormalDist for the bivariate normal distribution using Genz's algorithm as described in.
BiStudentDist	Extends the class ContinuousDistribution2Dim for the standard bivariate Student's t distribution.
ContinuousDistribution2Dim	Classes implementing 2-dimensional continuous distributions should inherit from this class.
ContinuousDistributionMulti	Classes implementing continuous multi-dimensional distributions should inherit from this class.
DirichletDist	Implements the abstract class ContinuousDistributionMulti for the Dirichlet distribution with parameters (α1,...,αd), αi > 0.
DiscreteDistributionIntMulti	Classes implementing multi-dimensional discrete distributions over the integers should inherit from this class.
MultinomialDist	Implements the abstract class DiscreteDistributionIntMulti for the multinomial distribution with parameters n and (p1, ...,pd).
MultiNormalDist	Implements the abstract class ContinuousDistributionMulti for the multinormal distribution with mean vector μ and covariance matrix Σ.
NegativeMultinomialDist	Implements the class DiscreteDistributionIntMulti for the negative multinomial distribution with parameters n > 0 and ( p1,…, pd) such that all 0 < pi < 1 and ∑i=1dpi < 1.

Package umontreal.iro.lecuyer.probdistmulti Description

This package contains Java classes providing methods to compute mass, density, distribution and complementary distribution functions for some multi-dimensional discrete and continuous probability distributions. It does not generate random numbers for multivariate distributions; for that, see the package randvarmulti.

Distributions

We recall that the distribution function of a continuous random vector X = {x₁, x₂,…, x_d} with density f (x₁, x₂,…, x_d) over the d-dimensional space R^d is

F(x1, x2,…, xd)	=	P[X1 <= x1, X2 <= x2,…, Xd <= xd]
	=	∫-∞x1∫-∞x2 ... ∫-∞xdf (s1, s2,…, sd) ds1ds2…dsd

while that of a discrete random vector X with mass function {p₁, p₂,…, p_d} over a fixed set of real numbers is

F(x1, x2,…, xd)	=	P[X1 <= x1, X2 <= x2,…, Xd <= xd]
	=	∑i1 <= x1∑i2 <= x2 ... ∑id <= xdp(x1, x2,…, xd),

where p(x₁, x₂,…, x_d) = P[X₁ = x₁, X₂ = x₂,…, X_d = x_d]. For a discrete distribution over the set of integers, one has

F(x1, x2,…, xd)	=	P[X1 <= x1, X2 <= x2,…, Xd <= xd]
	=	∑s1=-∞x1∑s2=-∞x2 ... ∑sd=-∞xdp(s1, s2,…, sd),

where p(s₁, s₂,…, s_d) = P[X₁ = s₁, X₂ = s₂,…, X_d = s_d].

We define bar(F), the complementary distribution function of X, as

bar(F)(x₁, x₂,…, x_d) = P[X₁ >= x₁, X₂ >= x₂,…, X_d >= x_d].