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Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables

Author

Listed:
  • Deheuvels, Paul
  • Puri, Madan L.
  • Ralescu, Stefan S.

Abstract

This paper concerns an asymptotic expansion for the distribution of the sum of independent zero-one random variables in case where this surn has variance [sigma]n2 --> [infinity]. The expansion presented is given to the order O([sigma]n-2). An application to the study of the exact rate of convergence in the central limit theorem for intermediate order statistics is included.

Suggested Citation

  • Deheuvels, Paul & Puri, Madan L. & Ralescu, Stefan S., 1989. "Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 282-303, February.
    • Handle: RePEc:eee:jmvana:v:28:y:1989:i:2:p:282-303
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    Cited by:

    1. Alessio Farcomeni & Monia Ranalli & Sara Viviani, 2021. "Dimension reduction for longitudinal multivariate data by optimizing class separation of projected latent Markov models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 462-480, June.
    2. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    3. Jean-Christophe Breton & Youssef El-Khatib & Jun Fan & Nicolas Privault, 2021. "A q-binomial extension of the CRR asset pricing model," Papers 2104.10163, arXiv.org, revised Feb 2023.
    4. Gradwohl, Ronen & Reingold, Omer, 2014. "Fault tolerance in large games," Games and Economic Behavior, Elsevier, vol. 86(C), pages 438-457.

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