Approximations for sums of three-valued 1-dependent symmetric random variables
Gabija Liaudanskaitė
Vilnius University
Vydas Čekanavičius
Vilnius University
Published 2020-07-01


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

How to Cite

Liaudanskaitė G. and Čekanavičius V. (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.


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.  

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please read the Copyright Notice in Journal Policy