Asymptotic Eulerian expansions for binomial and negative binomial reciprocals. (English) Zbl 0930.60004

Marciniak, Ewa; Wesolowski, Jacek

Proc. Am. Math. Soc. 127, No. 11, 3329-3338 (1999).

Summary: Asymptotic expansions of any order for expectations of inverses of random variables with positive binomial and negative binomial distributions are obtained in terms of the Eulerian polynomials. The paper extends and improves upon an expansion due to F. N. David and N. L. Johnson [Metron 18, No. 1/2, 77-81 (1956; Zbl 0074.35601)].

MSC:

60E05	Probability distributions: general theory
11B68	Bernoulli and Euler numbers and polynomials
05A16	Asymptotic enumeration
62E20	Asymptotic distribution theory in statistics

Keywords:

Eulerian numbers; Eulerian polynomials; asymptotic series expansions; inverse moments; positive binomial distribution; negative binomial distribution

Citations:

Zbl 0074.35601