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Asymptotic factorial powers expansions for binomial and negative binomial reciprocals |
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| Authors: | Grzegorz A. Rempala |
| Affiliation: | Department of Mathematics, University of Louisville, Louisville, Kentucky 40292 |
| Abstract: | By considering the variance formula for a shifted reciprocal of a binomial proportion, the asymptotic expansions of any order for first negative moments of binomial and negative binomial distributions truncated at zero are obtained. The expansions are given in terms of the factorial powers of the number of trials  . The obtained formulae are more accurate than those of Marciniak and Weso owski (1999) and simpler, as they do not involve the Eulerian polynomials. |
| Keywords: | Factorial power asymptotic expansions indirect estimator inverse moments elementary symmetric polynomial positive binomial distribution truncated negative binomial distribution |
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