|
Asymptotic factorial powers expansions for binomial and negative binomial reciprocals
Author(s):
Grzegorz
A.
Rempala
Journal:
Proc. Amer. Math. Soc.
132
(2004),
261-272.
MSC (2000):
Primary 60E05, 62E20;
Secondary 11B15, 05A16
Posted:
August 13, 2003
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 1.
- R. R. Bahadur (1960).
Some approximations to the binomial distribution function.
Ann. Math. Statist., 31:43-54. MR 22:11424 - 2.
- W. G. Cochran (1977).
Sampling Techniques.
Wiley Series in Probablity and Mathematical Statistics, John Wiley and Sons, New York. MR 57:14212 - 3.
- F. N. David and N. L. Johnson (1956-1957).
Reciprocal Bernoulli and Poisson variables.
Metron 18: 77-81. MR 18:520g - 4.
- E. W. Frees (1989).
Infinite order  -statistics.
Scand. J. Statist., 16(1):29-45. MR 90h:62047 - 5.
- R. L. Graham, D. E. Knuth and O. Patashnik (1994).
Concrete Mathematics.
Addison-Wesley Publishing Company, Reading, MA, second edition. MR 97d:68003 - 6.
- M. C. Jones (1987).
Inverse factorial moments.
Statistics and Probability Letters 6: 37-42. MR 90e:62025a - 7.
- E. Marciniak and J. Weso
 owski (1999).
Asymptotic Eulerian expansions for binomial and negative binomial reciprocals.
Proc. Amer. Math. Soc., 127(11):3329-3338. MR 2000b:60033 - 8.
- G. Rempala and G. Székely (1998).
On estimation with elementary symmetric polynomials.
Random Oper. Stochastic Equations, 6(1):77-88. MR 99e:62025 - 9.
- E. B. Rockower (1988).
Integral identities for random variables.
American Statistician 42: 68-72. MR 89a:60041 - 10.
- R. J. Serfling (1980).
Approximation Theorems of Mathematical Statistics.
Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons, New York. MR 82a:62003
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
60E05, 62E20,
11B15, 05A16
Retrieve articles in all Journals with MSC
(2000):
60E05, 62E20,
11B15, 05A16
Additional Information:
Grzegorz
A.
Rempala
Affiliation:
Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email:
grzes@louisville.edu
DOI:
10.1090/S0002-9939-03-07254-X
PII:
S 0002-9939(03)07254-X
Keywords:
Factorial power,
asymptotic expansions,
indirect estimator,
inverse moments,
elementary symmetric polynomial,
positive binomial distribution,
truncated negative binomial distribution
Received by editor(s):
March 1, 2001
Received by editor(s) in revised form:
August 1, 2002
Posted:
August 13, 2003
Dedicated:
To my parents
Communicated by:
Richard A. Davis
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org