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## 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 abstract class `DiscreteDistributionIntMulti` for the negative multinomial distribution with parameters γ > 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,…, xd} with density f (x1, x2,…, xd) over the d-dimensional space Rd 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,…, pd} 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,…, xd) = P[X1 = x1, X2 = x2,…, Xd = xd]. 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,…, sd) = P[X1 = s1, X2 = s2,…, Xd = sd].

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

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

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