Negative multinomial distribution

A demo of random number generation, density evaluation, and distribution fitting for the negative mutlinomial distribution

Contents

Generate negative multinomial random vectors

clear;
% reset random seed
s = RandStream('mt19937ar','Seed',1);
RandStream.setGlobalStream(s);
% sample size
n = 100;
% # bins
d = 5;
% prob parameter
prob = repmat(1/(d+1),1,d+1);
% overdispersion
b = 2;
% generate random vectors
X = negmnrnd(prob,b,n);

Evaluate negative multinomial pdf at true parameter value

logL = negmnpdfln(X,prob,b);
display(sum(logL));

 -859.4829

Fit negative multinomial distribution

tic;
[p_hat, b_hat, stats] = negmnfit(X);
toc;
display([p_hat, b_hat]);
display(stats.se');
display(stats);

figure;
plot(stats.logL_iter);
xlabel('iteration');
ylabel('log-likelihood');

Elapsed time is 0.024200 seconds.
    0.1787    0.1647    0.1522    0.1506    0.1531    0.2007    2.4261

    0.0127    0.0122    0.0117    0.0116    0.0117    0.4274


stats = 

  struct with fields:

           BIC: 1.7410e+03
           AIC: 1.7293e+03
    iterations: 4
      gradient: [6×1 double]
          logL: -856.6715
     logL_iter: [-856.7447 -856.6721 -856.6715 -856.6715]
            se: [6×1 double]
           dof: 6

Published with MATLAB® R2017a