Skewness for Maximum Likelihood Estimators of the Negative Binomial Distribution
- ORNL
The probability generating function of one version of the negative binomial distribution being (p + 1 - pt){sup -k}, we study elements of the Hessian and in particular Fisher's discovery of a series form for the variance of k, the maximum likelihood estimator, and also for the determinant of the Hessian. There is a link with the Psi function and its derivatives. Basic algebra is excessively complicated and a Maple code implementation is an important task in the solution process. Low order maximum likelihood moments are given and also Fisher's examples relating to data associated with ticks on sheep. Efficiency of moment estimators is mentioned, including the concept of joint efficiency. In an Addendum we give an interesting formula for the difference of two Psi functions.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- Work for Others (WFO)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 931488
- Journal Information:
- Far East Journal of Theoretical Statistics, Vol. 22, Issue 1
- Country of Publication:
- United States
- Language:
- English
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