The Difference Calculus and The NEgative Binomial Distribution
- ORNL
- University of Georgia, Athens, GA
In a previous paper we state the dominant term in the third central moment of the maximum likelihood estimator k of the parameter k in the negative binomial probability function where the probability generating function is (p + 1 - pt){sup -k}. A partial sum of the series {Sigma}1/(k + x){sup 3} is involved, where x is a negative binomial random variate. In expectation this sum can only be found numerically using the computer. Here we give a simple definite integral in (0,1) for the generalized case. This means that now we do have a valid expression for {radical}{beta}{sub 11}(k) and {radical}{beta}{sub 11}(p). In addition we use the finite difference operator {Delta}, and E = 1 + {Delta} to set up formulas for low order moments. Other examples of the operators are quoted relating to the orthogonal set of polynomials associated with the negative binomial probability function used as a weight function.
- Research Organization:
- Oak Ridge National Laboratory (ORNL)
- Sponsoring Organization:
- ORNL work for others
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 931596
- Journal Information:
- Far East Journal of Theoretical Statistics, Journal Name: Far East Journal of Theoretical Statistics
- Country of Publication:
- United States
- Language:
- English
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