umontreal.iro.lecuyer.probdistmulti

Class DiscreteDistributionIntMulti

java.lang.Object

umontreal.iro.lecuyer.probdistmulti.DiscreteDistributionIntMulti

Direct Known Subclasses:

MultinomialDist, NegativeMultinomialDist

public abstract class DiscreteDistributionIntMulti
extends java.lang.Object

Classes implementing multi-dimensional discrete distributions over the integers should inherit from this class. It specifies the signature of methods for computing the mass function (or probability) p(x₁, x₂,…, x_d) = P[X₁ = x₁, X₂ = x₂,…, X_d = x_d] and the cumulative probabilities for a random vector X with a discrete distribution over the integers.

Constructor Summary

Constructors

Constructor and Description
DiscreteDistributionIntMulti()

Method Summary

Modifier and Type	Method and Description
double	cdf(int[] x) Computes the cumulative probability function F of the distribution evaluated at x, assuming the lowest values start at 0, i.e.
abstract double[][]	getCorrelation() Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.
abstract double[][]	getCovariance() Returns the variance-covariance matrix of the distribution, defined as σij = E[(Xi - μi)(Xj - μj)].
int	getDimension() Returns the dimension d of the distribution.
abstract double[]	getMean() Returns the mean vector of the distribution, defined as μi = E[Xi].
abstract double	prob(int[] x) Returns the probability mass function p(x1, x2,…, xd), which should be a real number in [0, 1].

Methods inherited from class java.lang.Object

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

Constructor Detail

DiscreteDistributionIntMulti

public DiscreteDistributionIntMulti()

Method Detail

prob

public abstract double prob(int[] x)

Returns the probability mass function p(x₁, x₂,…, x_d), which should be a real number in [0, 1].

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

cdf

public double cdf(int[] x)

Computes the cumulative probability function F of the distribution evaluated at x, assuming the lowest values start at 0, i.e. computes

F(x₁, x₂,…, x_d) = ∑_s1=0^x₁∑_s2=0^{x₂ ...} ∑_sd=0^x_dp(s₁, s₂,…, s_d).

Uses the naive implementation, is very inefficient and may underflows.

getDimension

public int getDimension()

Returns the dimension d of the distribution.

getMean

public abstract double[] getMean()

Returns the mean vector of the distribution, defined as μ_i = E[X_i].

getCovariance

public abstract double[][] getCovariance()

Returns the variance-covariance matrix of the distribution, defined as
σ_ij = E[(X_i - μ_i)(X_j - μ_j)].

getCorrelation

public abstract double[][] getCorrelation()

Returns the correlation matrix of the distribution, defined as ρ_ij = σ_ij/(σ_iiσ_jj)^1/2.