I wonder if your code is correct?

I ran your script until an error was reported. the data set
of 30 obs was


[1] 0 0 1 3 3 3 4 4 4 4 5 5 5 5 5 7 7 7 7 7 7 8 9 10 11
[26] 12 12 12 15 16

I created a tiny AD Model Builder program to do MLE on it.

DATA_SECTION
  init_int nobs
  init_vector y(1,nobs)
PARAMETER_SECTION
  init_number log_mu
  init_number log_alpha
  sdreport_number mu
  sdreport_number tau
  objective_function_value f
PROCEDURE_SECTION
  mu=exp(log_mu);
  tau=1.0+exp(log_alpha);
  for (int i=1;i<=nobs;i++)
  {
    f-=log_negbinomial_density(y(i),mu,tau);
  }
It converged quickly and

The eigenvalues of the Hessian were

    4.711089774    78.27632341

and the estimates and std devs of the parameters mu and tau were

index   name       value      std dev

     3   mu         6.6000e+00 7.7318e-01
     4   tau        2.7173e+00 7.8944e-01

where tau is the variance divided by the mean.

This was all so simple that I suspect your (rather difficult to read)
R code is wrong, otherwise R must really suck at this kind of problem.

      Dave

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