Infinitely Divisible Approximations for Sums of m-Dependent Random Variables

P. Vellaisamy () and V. Čekanavičius ()
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P. Vellaisamy: Indian Institute of Technology Bombay
V. Čekanavičius: Vilnius University

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 2432-2445

Abstract: 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.

Keywords: Compound Poisson distribution; Uniform Kolmogorov theorem; m-dependent variables; Total variation norm; Local norm; 60F05; 60G50 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0774-0

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