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    Method of moments and maximum likelihood for NegBinomial

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    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.

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

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    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.

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