# Method of moments and maximum likelihood for NegBinomial

Students are given addition items and the number of items the students get wrong prior to getting their 25th correct item is recorded. If X is the number of incorrect items, then it has a negative binomial distribution with pdf (seen in attachment). Consider a random sample X1, ..., Xn from this distribution:

a. Find the maximum likelihood estimator of p.

b. Find the maximum likelihood estimator of the log-odds log (p/1-p)

c. Find the method of moments estimator of the log-odds.

d. Find the fisher information about p.

e. Find an approximate standard error of the MLE of p based on the Fisher information.

f. Find an approximate standard error of the MLE of the log-odds.

https://brainmass.com/statistics/sampling-distribution/method-moments-maximum-likelihood-negbinomial-567785

#### Solution Summary

The solution gives detailed steps on determining method of moments, method of maximum likelihood and fisher information. All formulas and calculations are shown and explained.