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The concept of weak exchangeability and its applications

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  • Serkan Eryilmaz

    (Atilim University)

Abstract

A finite sequence of binary random variables is called a weak exchangeable sequence of order m if the sequence consists of m random vectors such that the elements within each random vector are exchangeable in the usual sense and the different random vectors are dependent. The exact and asymptotic joint distributions of the m-dimensional random vector whose elements include the number of successes in each exchangeable sequence are derived. Potential applications of the concept of weak exchangeability are discussed with illustrative examples.

Suggested Citation

  • Serkan Eryilmaz, 2017. "The concept of weak exchangeability and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 259-271, April.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:3:d:10.1007_s00184-016-0602-z
    DOI: 10.1007/s00184-016-0602-z
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    References listed on IDEAS

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    1. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
    2. Zaigraev, Alexander & Kaniovski, Serguei, 2010. "Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1079-1084, July.
    3. Navarro, Jorge & Spizzichino, Fabio & Balakrishnan, N., 2010. "Applications of average and projected systems to the study of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1471-1482, July.
    4. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    5. Lau, Tai Shing, 1992. "The reliability of exchangeable binary systems," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 153-158, January.
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    Cited by:

    1. Eryilmaz, Serkan, 2018. "On success runs in a sequence of dependent trials with a change point," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 91-98.
    2. Somayeh Ashrafi & Majid Asadi & Jorge Navarro, 2022. "Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1485-1502, September.
    3. Eryilmaz, Serkan & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2018. "Marginal and joint reliability importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 118-128.
    4. Hindolo George-Williams & Geng Feng & Frank PA Coolen & Michael Beer & Edoardo Patelli, 2019. "Extending the survival signature paradigm to complex systems with non-repairable dependent failures," Journal of Risk and Reliability, , vol. 233(4), pages 505-519, August.
    5. Anastasios N. Arapis & Frosso S. Makri & Zaharias M. Psillakis, 2017. "Joint distribution of k-tuple statistics in zero-one sequences of Markov-dependent trials," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    6. Serkan Eryilmaz & Frank P.A. Coolen & Tahani Coolen‐Maturi, 2018. "Mean residual life of coherent systems consisting of multiple types of dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 86-97, February.
    7. Tavangar, Mahdi & Hashemi, Marzieh, 2022. "Reliability and maintenance analysis of coherent systems subject to aging and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).

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