umontreal.iro.lecuyer.probdistmulti
Class NegativeMultinomialDist

java.lang.Object
  umontreal.iro.lecuyer.probdistmulti.DiscreteDistributionIntMulti
      umontreal.iro.lecuyer.probdistmulti.NegativeMultinomialDist

public class NegativeMultinomialDist
extends DiscreteDistributionIntMulti

Implements the class DiscreteDistributionIntMulti for the negative multinomial distribution with parameters n > 0 and ( p₁,…, p_d) such that all 0 < p_i < 1 and ∑_i=1^dp_i < 1. The probability mass function is

P[X = (x₁,…, x_d)] = (Γ(n+∑_i=1^dx_i)/Γ(n))p₀ⁿ∏_i=1^dp_i^x_i/x_i!

where p₀ = 1 - ∑_i=1^dp_i.

Constructor Summary

NegativeMultinomialDist(double n, double[] p)
Creates a NegativeMultinomialDist object with parameters n and (p₁, ..., p_d) such that ∑_i=1^dp_i < 1, as described above.

Method Summary

static double	cdf(double n, double[] p, int[] x) Computes the cumulative probability function F of the negative multinomial distribution with parameters n and (p1, ..., pk), evaluated at x.
double[][]	getCorrelation() Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.
static double[][]	getCorrelation(double n, double[] p) Computes the correlation matrix of the negative multinomial distribution with parameters n and (p1, ..., pd).
double[][]	getCovariance() Returns the variance-covariance matrix of the distribution, defined as σij = E[(Xi - μi)(Xj - μj)].
static double[][]	getCovariance(double n, double[] p) Computes the covariance matrix of the negative multinomial distribution with parameters n and (p1, ..., pd).
double	getGamma() Returns the parameter n of this object.
double[]	getMean() Returns the mean vector of the distribution, defined as μi = E[Xi].
static double[]	getMean(double n, double[] p) Computes the mean E[X] = npi/p0 of the negative multinomial distribution with parameters n and (p1, ..., pd).
static double[]	getMLE(int[][] x, int m, int d) Estimates and returns the parameters [hat(n), hat(p)1, ..., hat(p)d] of the negative multinomial distribution using the maximum likelihood method.
static double	getMLEninv(int[][] x, int m, int d) Estimates and returns the parameter ν = 1/hat(n) of the negative multinomial distribution using the maximum likelihood method.
double[]	getP() Returns the parameters (p1, ..., pd) of this object.
static double	prob(double n, double[] p, int[] x) Computes the probability mass function of the negative multinomial distribution with parameters n and (p1, ..., pd), evaluated at x.
double	prob(int[] x) Returns the probability mass function p(x1, x2,…, xd), which should be a real number in [0, 1].
void	setParams(double n, double[] p) Sets the parameters n and (p1, ..., pd) of this object.

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.DiscreteDistributionIntMulti

cdf, getDimension

Methods inherited from class java.lang.Object

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

Constructor Detail

NegativeMultinomialDist

public NegativeMultinomialDist(double n,
                               double[] p)

Creates a NegativeMultinomialDist object with parameters n and (p₁, ..., p_d) such that ∑_i=1^dp_i < 1, as described above. We have p_i = p[i-1].

Method Detail

prob

public double prob(int[] x)

Description copied from class: DiscreteDistributionIntMulti

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

Specified by:

prob in class DiscreteDistributionIntMulti

Parameters:

x - value at which the mass function must be evaluated

Returns:

the mass function evaluated at x

getMean

public double[] getMean()

Description copied from class: DiscreteDistributionIntMulti

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

Specified by:

getMean in class DiscreteDistributionIntMulti

getCovariance

public double[][] getCovariance()

Description copied from class: DiscreteDistributionIntMulti

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

Specified by:

getCovariance in class DiscreteDistributionIntMulti

getCorrelation

public double[][] getCorrelation()

Description copied from class: DiscreteDistributionIntMulti

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

Specified by:

getCorrelation in class DiscreteDistributionIntMulti

prob

public static double prob(double n,
                          double[] p,
                          int[] x)

Computes the probability mass function of the negative multinomial distribution with parameters n and (p₁, ..., p_d), evaluated at x.

cdf

public static double cdf(double n,
                         double[] p,
                         int[] x)

Computes the cumulative probability function F of the negative multinomial distribution with parameters n and (p₁, ..., p_k), evaluated at x.

getMean

public static double[] getMean(double n,
                               double[] p)

Computes the mean E[X] = np_i/p₀ of the negative multinomial distribution with parameters n and (p₁, ..., p_d).

getCovariance

public static double[][] getCovariance(double n,
                                       double[] p)

Computes the covariance matrix of the negative multinomial distribution with parameters n and (p₁, ..., p_d).

getCorrelation

public static double[][] getCorrelation(double n,
                                        double[] p)

Computes the correlation matrix of the negative multinomial distribution with parameters n and (p₁, ..., p_d).

getMLE

public static double[] getMLE(int[][] x,
                              int m,
                              int d)

Estimates and returns the parameters [hat(n), hat(p)₁, ..., hat(p)_d] of the negative multinomial distribution using the maximum likelihood method. It uses the m observations of d components in table x[i][j], i = 0, 1,…, m - 1 and j = 0, 1,…, d - 1.

Parameters:

x - the list of observations used to evaluate parameters

m - the number of observations used to evaluate parameters

d - the dimension of each vector

Returns:

returns the parameters [hat(n), hat(p)₁, ..., hat(p)_d]

getMLEninv

public static double getMLEninv(int[][] x,
                                int m,
                                int d)

Estimates and returns the parameter ν = 1/hat(n) of the negative multinomial distribution using the maximum likelihood method. It uses the m observations of d components in table x[i][j], i = 0, 1,…, m - 1 and j = 0, 1,…, d - 1.

Parameters:

x - the list of observations used to evaluate parameters

m - the number of observations used to evaluate parameters

d - the dimension of each vector

Returns:

returns the parameter 1/hat(n)

getGamma

public double getGamma()

Returns the parameter n of this object.

getP

public double[] getP()

Returns the parameters (p₁, ..., p_d) of this object.

setParams

public void setParams(double n,
                      double[] p)

Sets the parameters n and (p₁, ..., p_d) of this object.