Asymptotic expansions for inverse moments of binomial and negative binomial

Wuyungaowa,; Wang, Tianming

doi:10.1016/j.spl.2008.05.030

Cited by 10 publications

(3 citation statements)

References 6 publications

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“…It follows that µ([0, ǫ)) ≤ ν([0, ǫ)) for all ǫ > 0. Then, by using Lemma 3.9, the result in Example 3.6 and Theorem 1 in Wuyungaowa and Wang (2008)…”

Section: Power Decaymentioning

confidence: 96%

Inheritance of strong mixing and weak dependence under renewal sampling

Brandes¹,

Curato²,

Stelzer³

2020

Preprint

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Let X be a continuous-time strongly mixing or weakly dependent process and T a renewal process independent of X with inter-arrival times {τ i }. We show general conditions under which the sampled process (X T i , τ i ) ⊤ is strongly mixing or weakly dependent. Moreover, we explicitly compute the strong mixing or weak dependence coefficients of the renewal sampled process and show that exponential or power decay of the coefficients of X is preserved (at least asymptotically). Our results imply that essentially all central limit theorems available in the literature for strongly mixing or weakly dependent processes can be applied when renewal sampled observations of the process X are at disposal.

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“…It follows that µ([0, ǫ)) ≤ ν([0, ǫ)) for all ǫ > 0. Then, by using Lemma 3.9, the result in Example 3.6 and Theorem 1 in Wuyungaowa and Wang (2008)…”

Section: Power Decaymentioning

confidence: 96%

Inheritance of strong mixing and weak dependence under renewal sampling

Brandes¹,

Curato²,

Stelzer³

2020

Preprint

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“…Combined with the exponentially small items (17), (18), (19) and (20) Note that the inner sum over k is curtailed because the degree of µ n is at most ⌊n/2⌋, i.e., c kn = 0 if k ≤ ⌊(n + 1)/2⌋. As a consequence of (7), the term corresponding to n = 2M − 1 in the outer sum is written as O(G(x)x −M ) in the last equality.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…for real r by substituting a = 0 in the right hand side of (14). Expansions for (15) have been considered by Marciniak and Wesolowski [14] and Rempala [15] for the special case r = 1, and by Wuyungaowa and Wang [18] for integer r ≥ 0.…”

Section: A General Versionmentioning

confidence: 99%

On an asymptotic series of Ramanujan

2009

Ramanujan J

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An asymptotic series in Ramanujan's second notebook (Entry 10, Chap. 3) is concerned with the behavior of the expected value of φ(X) for large λ where X is a Poisson random variable with mean λ and φ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of φ(X) when the distribution of X belongs to a suitable family indexed by a convolution parameter. Examples include the binomial, negative binomial, and gamma families. Some formulas associated with the negative binomial appear new.

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Probabilistic Analysis of Hierarchical Cluster Protocols for Wireless Sensor Networks

Kaj

2009

Lecture Notes in Computer Science

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Asymptotic expansions for inverse moments of binomial and negative binomial

Cited by 10 publications

References 6 publications

Inheritance of strong mixing and weak dependence under renewal sampling

Inheritance of strong mixing and weak dependence under renewal sampling

On an asymptotic series of Ramanujan

Probabilistic Analysis of Hierarchical Cluster Protocols for Wireless Sensor Networks

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