论文信息 - ASYMPTOTIC EXPANSION FOR INVERSE MOMENTS OF BINOMIAL AND POISSON DISTRIBUTIONS

ASYMPTOTIC EXPANSION FOR INVERSE MOMENTS OF BINOMIAL AND POISSON DISTRIBUTIONS

An asymptotic expansion for inverse moments of positive bino- mial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribu- tion. Compared to previous results, a single expansion formula covers all (also non-integer) inverse moments. In addition, the approach can be generalized to other positive distributions.

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[1] Anatoly Zhigljavsky,et al. Approximating the negative moments of the Poisson distribution , 2004 .

[2] Grzegorz A. Rempala,et al. Asymptotic factorial powers expansions for binomial and negative binomial reciprocals , 2003 .

[3] Nancy L. Garcia,et al. On inverse moments of nonnegative random variables , 2001 .

[4] Jacek Wesołowski,et al. Asymptotic Eulerian expansions for binomial and negative binomial reciprocals , 1999 .

[5] E. Rockower. Integral identities for random variables , 1988 .

[6] N. Cressie,et al. The Moment-Generating Function and Negative Integer Moments , 1981 .

[7] D. G. Kabe. Inverse moments of discrete distributions , 1976 .

[8] M. Chao,et al. Negative Moments of Positive Random Variables , 1972 .

[9] M. Tiku. A Note on the Negative Moments of a Truncated Poisson Variate , 1964 .

[10] Z. Govindarajulu. Recurrence Relations for the Inverse Moments of the Positive Binomial Variable , 1963 .

[11] W. Mendenhall,et al. An Approximation to the Negative Moments of the Positive Binomial Useful in Life Testing , 1960 .

[12] I. Richard Savage,et al. Tables of the Expected Value of 1/X for Positive Bernoulli and Poisson Variables , 1954 .

[13] Frederick F. Stephan,et al. The Expected Value and Variance of the Reciprocal and Other Negative Powers of a Positive Bernoullian Variate , 1945 .