NegativeMultinomialDist (Java Libraries for Stochastic Simulation)

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

```
public class NegativeMultinomialDist
extends DiscreteDistributionIntMulti
```
Implements the abstract class DiscreteDistributionIntMulti for the negative multinomial distribution with parameters γ > 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(γ+∑_i=1^dx_i)/Γ(γ)∏_i=1^dx_i!)p₀^γ∏_i=1^dp_i^x_i
where p₀ = 1 - ∑_i=1^dp_i.

Constructor Summary

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

Method Summary

Methods
Modifier and Type	Method and Description
`static double`	`cdf(double gamma, double[] p, int[] x)` Computes the cumulative probability function F of the negative multinomial distribution with parameters γ and (p₁,...,p_k), evaluated at x.
`double[][]`	`getCorrelation()` Returns the correlation matrix of the distribution, defined as ρ_ij = σ_ij/(σ_iiσ_jj)^1/2.
`static double[][]`	`getCorrelation(double gamma, double[] p)` Computes the correlation matrix of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
`double[][]`	`getCovariance()` Returns the variance-covariance matrix of the distribution, defined as σ_ij = E[(X_i - μ_i)(X_j - μ_j)].
`static double[][]`	`getCovariance(double gamma, double[] p)` Computes the covariance matrix of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
`double`	`getGamma()` Returns the parameter γ of this object.
`static double[]`	`getMaximumLikelihoodEstimate(int[][] x, int n, int d)` Deprecated.
`double[]`	`getMean()` Returns the mean vector of the distribution, defined as μ_i = E[X_i].
`static double[]`	`getMean(double gamma, double[] p)` Computes the mean E[X] = γp_i/p₀ of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
`static double[]`	`getMLE(int[][] x, int n, int d)` Estimates and returns the parameters [ hat(γ), hat(p_1),..., hat(p_d)] of the negative multinomial distribution using the maximum likelihood method.
`double[]`	`getP()` Returns the parameters (p₁,...,p_d) of this object.
`static double`	`prob(double gamma, double[] p, int[] x)` Computes the probability mass function of the negative multinomial distribution with parameters γ and (p₁,...,p_d), evaluated at x.
`double`	`prob(int[] x)` Returns the probability mass function p(x₁, x₂,…, x_d), which should be a real number in [0, 1].
`void`	`setParams(double gamma, double[] p)` Sets the parameters γ and (p₁,...,p_d) 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 gamma,
                       double[] p)
```
    Creates a NegativeMultinomialDist object with parameters γ = gamma 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 gamma,
          double[] p,
          int[] x)
```
    Computes the probability mass function of the negative multinomial distribution with parameters γ and (p₁,...,p_d), evaluated at x.
  - cdf
```
public static double cdf(double gamma,
         double[] p,
         int[] x)
```
    Computes the cumulative probability function F of the negative multinomial distribution with parameters γ and (p₁,...,p_k), evaluated at x.
  - getMean
```
public static double[] getMean(double gamma,
               double[] p)
```
    Computes the mean E[X] = γp_i/p₀ of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
  - getCovariance
```
public static double[][] getCovariance(double gamma,
                       double[] p)
```
    Computes the covariance matrix of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
  - getCorrelation
```
public static double[][] getCorrelation(double gamma,
                        double[] p)
```
    Computes the correlation matrix of the negative multinomial distribution with parameters γ and (p₁,...,p_d).
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(int[][] x,
                                               int n,
                                               int d)
```
    Deprecated.
    
    It is now called getMLE.
  - getMLE
```
public static double[] getMLE(int[][] x,
              int n,
              int d)
```
    Estimates and returns the parameters [ hat(γ), hat(p_1),..., hat(p_d)] of the negative multinomial distribution using the maximum likelihood method. It uses the n observations of d components in table x[i][j], i = 0, 1,…, n - 1 and j = 0, 1,…, d - 1.
    
    Parameters:
    x - the list of observations used to evaluate parameters
    n - the number of observations used to evaluate parameters
    d - the dimension of each vector
    
    Returns:
    returns the parameters [ hat(γ), hat(p_1),...,hat(p_d)]
  - getGamma
```
public double getGamma()
```
    Returns the parameter γ of this object.
  - getP
```
public double[] getP()
```
    Returns the parameters (p₁,...,p_d) of this object.
  - setParams
```
public void setParams(double gamma,
             double[] p)
```
    Sets the parameters γ and (p₁,...,p_d) of this object.

Class NegativeMultinomialDist

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

NegativeMultinomialDist

Method Detail

prob

getMean

getCovariance

getCorrelation

prob

cdf

getMean

getCovariance

getCorrelation

getMaximumLikelihoodEstimate

getMLE

getGamma

getP

setParams