Normal approximation for sum of random number of summands
Articles
Leonas Saulis
Vilnius Gediminas Technical University
Dovilė Deltuvienė
Vilnius Gediminas Technical University
Published 2021-06-01
https://doi.org/10.15388/LMR.2007.24257
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Keywords

distribution function
characteristic function
cumulant
large deviations
exponential inequality

How to Cite

Saulis L. and Deltuvienė D. (2021) “Normal approximation for sum of random number of summands”, Lietuvos matematikos rinkinys, 47(spec.), pp. 531–536. doi: 10.15388/LMR.2007.24257.

Abstract

Normal aproximationof sum ZtNti=1Xi of i.i.d. random variables (r.v.) Xi , i = 1, 2, . . . with mean EXi = μ and variance DXi = σ2 > 0 is analyzed taking into consideration large deviations. Here Nt is non-negative integer-valued random variable, which depends on t , but not depends at Xi , i = 1, 2, . . ..

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