MultinomialDist (Java Libraries for Stochastic Simulation)

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

```
public class MultinomialDist
extends DiscreteDistributionIntMulti
```
Implements the abstract class DiscreteDistributionIntMulti for the multinomial distribution with parameters n and (p₁, ...,p_d). The probability mass function is

P[X = (x₁,..., x_d)] = n!∏_i=1^dp_i^x_i/(∏_i=1^dx_i!),
where ∑_i=1^dx_i = n and ∑_i=1^dp_i = 1.

Constructor Summary

Constructors
Constructor and Description

MultinomialDist(int n, double[] p)
Creates a MultinomialDist object with parameters n and (p₁,...,p_d) such that ∑_i=1^dp_i = 1.

Constructors
Constructor and Description
`MultinomialDist(int n, double[] p)` Creates a `MultinomialDist` object with parameters n and (p₁,...,p_d) such that ∑_i=1^dp_i = 1.

Method Summary

Methods
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.
`static double`	`cdf(int n, double[] p, int[] x)` Computes the function F of the multinomial distribution with parameters n and (p₁,...,p_d) 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(int n, double[] p)` Computes the correlation matrix of the multinomial distribution with parameters n 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(int n, double[] p)` Computes the covariance matrix of the multinomial distribution with parameters n and (p₁,...,p_d).
`static double[]`	`getMaximumLikelihoodEstimate(int[][] x, int m, int d, int n)` Deprecated.
`double[]`	`getMean()` Returns the mean vector of the distribution, defined as μ_i = E[X_i].
`static double[]`	`getMean(int n, double[] p)` Computes the mean E[X_i] = np_i of the multinomial distribution with parameters n and (p₁,...,p_d).
`static double[]`	`getMLE(int[][] x, int m, int d, int n)` Estimates and returns the parameters [hat(p_i),...,hat(p_d)] of the multinomial distribution using the maximum likelihood method.
`int`	`getN()` Returns the parameter n of this object.
`double[]`	`getP()` Returns the parameters (p₁,...,p_d) of this object.
`double`	`prob(int[] x)` Returns the probability mass function p(x₁, x₂,…, x_d), which should be a real number in [0, 1].
`static double`	`prob(int n, double[] p, int[] x)` Computes the probability mass function of the multinomial distribution with parameters n and (p₁,...,p_d) evaluated at x.
`void`	`setParams(int n, double[] p)` Sets the parameters n and (p₁,...,p_d) of this object.

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

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - MultinomialDist
```
public MultinomialDist(int n,
               double[] p)
```
    Creates a MultinomialDist object with parameters n and (p₁,...,p_d) such that ∑_i=1^dp_i = 1. 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
  - cdf
```
public double cdf(int[] x)
```
    Description copied from class: DiscreteDistributionIntMulti
    
    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 ...}∑_{s_d=0}^x_dp(s₁, s₂,…, s_d).
    Uses the naive implementation, is very inefficient and may underflows.
    
    Overrides:
    
    cdf in class DiscreteDistributionIntMulti
  - 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(int n,
          double[] p,
          int[] x)
```
    Computes the probability mass function of the multinomial distribution with parameters n and (p₁,...,p_d) evaluated at x.
  - cdf
```
public static double cdf(int n,
         double[] p,
         int[] x)
```
    Computes the function F of the multinomial distribution with parameters n and (p₁,...,p_d) evaluated at x.
  - getMean
```
public static double[] getMean(int n,
               double[] p)
```
    Computes the mean E[X_i] = np_i of the multinomial distribution with parameters n and (p₁,...,p_d).
  - getCovariance
```
public static double[][] getCovariance(int n,
                       double[] p)
```
    Computes the covariance matrix of the multinomial distribution with parameters n and (p₁,...,p_d).
  - getCorrelation
```
public static double[][] getCorrelation(int n,
                        double[] p)
```
    Computes the correlation matrix of the multinomial distribution with parameters n and (p₁,...,p_d).
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(int[][] x,
                                               int m,
                                               int d,
                                               int n)
```
    Deprecated.
    
    It is now called getMLE.
  - getMLE
```
public static double[] getMLE(int[][] x,
              int m,
              int d,
              int n)
```
    Estimates and returns the parameters [hat(p_i),...,hat(p_d)] of the 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 observation
    n - the number of independant trials for each series
    
    Returns:
    returns the parameters [hat(p_i),...,hat(p_d)]
  - getN
```
public int getN()
```
    Returns the parameter n of this object.
  - getP
```
public double[] getP()
```
    Returns the parameters (p₁,...,p_d) of this object.
  - setParams
```
public void setParams(int n,
             double[] p)
```
    Sets the parameters n and (p₁,...,p_d) of this object.

Class MultinomialDist

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Detail

MultinomialDist

Method Detail

prob

cdf

getMean

getCovariance

getCorrelation

prob

cdf

getMean

getCovariance

getCorrelation

getMaximumLikelihoodEstimate

getMLE

getN

getP

setParams