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Infinitely Divisible Approximations for Sums of m-Dependent Random Variables

Author

Listed:
  • P. Vellaisamy

    (Indian Institute of Technology Bombay)

  • V. Čekanavičius

    (Vilnius University)

Abstract

Assuming conditions on factorial cumulants, we estimate the closeness of distribution of a sum of nonnegative integer-valued m-dependent random variables to the class of all infinitely divisible laws. The accuracy of approximation is measured in total variation and local metrics. Our results are exemplified by an analogue of the first uniform Kolmogorov theorem for the statistic of $$(k_1,k_2)$$ ( k 1 , k 2 ) events.

Suggested Citation

  • P. Vellaisamy & V. Čekanavičius, 2018. "Infinitely Divisible Approximations for Sums of m-Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2432-2445, December.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0774-0
    DOI: 10.1007/s10959-017-0774-0
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    References listed on IDEAS

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    1. Huang, Wen-Tao & Tsai, Chiou-Shiang, 1991. "On a modified binomial distribution of order k," Statistics & Probability Letters, Elsevier, vol. 11(2), pages 125-131, February.
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