Approximations for sums of three-valued 1-dependent symmetric random variables
Articles
Gabija Liaudanskaitė
Vilnius University
https://orcid.org/0000-0003-0194-9050
Vydas Čekanavičius
Vilnius University
https://orcid.org/0000-0002-8510-5578
Published 2020-07-01
https://doi.org/10.15388/namc.2020.25.16843
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Keywords

compound Poisson distribution
1-dependent variables
total variation norm
local norm
nonuniform estimate

How to Cite

LiaudanskaitėG. and ČekanavičiusV. (2020) “Approximations for sums of three-valued 1-dependent symmetric random variables”, Nonlinear Analysis: Modelling and Control, 25(4), pp. 675–691. doi: 10.15388/namc.2020.25.16843.

Abstract

The sum of symmetric three-point 1-dependent nonidentically distributed random variables is approximated by a compound Poisson distribution. The accuracy of approximation is estimated in the local and total variation norms. For distributions uniformly bounded from zero,
the accuracy of approximation is of the order O(n–1). In the general case of triangular arrays of identically distributed summands, the accuracy is at least of the order O(n1/2). Nonuniform estimates are obtained for distribution functions and probabilities. The characteristic function
method is used.  

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