C245. Inverse moments of negative- binomial distributions

Jones, M. C.

doi:10.1080/00949658608810874

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…where M(t) = (αe t /(1 − (1 − α)e t )) k is the moment generating function of the shifted negative binomial distribution. Then the implicit formula for μ k,1 is (Cressie et al, 1981;Jones, 1986) where Li 2 (α) is dilogarithm function, ψ (α) is digamma function, and γ is Euler-Mascheroni constant. Then E(α/α − 1) 2 = k 2 μ k,2 /α 2 − 2kμ k,1 /α + 1.…”

Section: A3 On the Adaptive Quantile Estimationmentioning

confidence: 99%

Signal localization: a new approach in signal discovery

et al. 2016

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A new approach for statistical association signal identification is developed in this paper. We consider a strategy for nonprecise signal identification by extending the well-known signal detection and signal identification methods applicable to the multiple testing problem. Collection of statistical instruments under the presented approach is much broader than under the traditional signal identification methods, allowing more efficient signal discovery. Further assessments of maximal value and average statistics in signal discovery are improved. While our method does not attempt to detect individual predictors, it instead detects sets of predictors that are jointly associated with the outcome. Therefore, an important application would be in genome wide association study (GWAS), where it can be used to detect genes which influence the phenotype but do not contain any individually significant single nucleotide polymorphism (SNP). We compare power of the signal identification method based on extremes of single p-values with the signal localization method based on average statistics for logarithms of p-values. A simulation analysis informs the application of signal localization using the average statistics for wide signals discovery in Gaussian white noise process. We apply average statistics and the localization method to GWAS to discover better gene influences of regulating loci in a Chinese cohort developed for risk of nasopharyngeal carcinoma (NPC).

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Section: A3 On the Adaptive Quantile Estimationmentioning

confidence: 99%

Signal localization: a new approach in signal discovery

et al. 2016

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“…Govindajarulu [12] has found recurrence relations between inverse moments of positive binomial variates and Refs. [17,21,30,31,24] contain various bounds on inverse moments. More general methods, valid for any distribution and involving integrals, have been proposed in [7,8,9,18,26].…”

Section: Introductionmentioning

confidence: 99%

Inverse moments of univariate discrete distributions via the Poisson expansion

Audenaert

2008

Preprint

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In this note we present a series expansion of inverse moments of a non-negative discrete random variate in terms of its factorial cumulants, based on the Poisson-Charlier expansion of a discrete distribution. We apply the general method to the positive binomial distribution and obtain a convergent series for its inverse moments with an error residual that is uniformly bounded on the entire interval 0 ≤ p ≤ 1.

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Inverse factorial moments

Jones

1987

Statistics & Probability Letters

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C245. Inverse moments of negative- binomial distributions

Cited by 5 publications

References 3 publications

Signal localization: a new approach in signal discovery

Signal localization: a new approach in signal discovery

Inverse moments of univariate discrete distributions via the Poisson expansion

Inverse factorial moments

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