On the Accuracy of the Exponential Approximation to Random Sums of Alternating Random Variables

Irina Shevtsova and Mikhail Tselishchev
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Irina Shevtsova: Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
Mikhail Tselishchev: Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2020, vol. 8, issue 11, 1-11

Abstract: Using the generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with a finite non-zero first moment, we prove moment-type error-bounds in the Kantorovich distance for the exponential approximation to random sums of possibly dependent random variables with positive finite expectations, in particular, to geometric random sums, generalizing the previous results to alternating and dependent random summands. We also extend the notions of new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) distributions to alternating random variables in terms of the corresponding distribution functions and provide a criteria in terms of conditional expectations similar to the classical one. As corollary, we provide simplified error-bounds in the case of NBUE/NWUE conditional distributions of random summands.

Keywords: Rényi theorem; Kantorovich distance; zeta-metrics; Stein’s method; stationary renewal distribution; equilibrium transform; geometric random sum; characteristic function; NBUE, NWUE distributions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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