On the normal approximation of a sum of a random number of independent random variables

2012 ◽  
Vol 52 (4) ◽  
pp. 435-443 ◽  
Author(s):  
Jonas Kazys Sunklodas
Keyword(s):  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Independent Random Variables

scholarly journals On the probabilities of large deviations for sums of random number of independent random variables

1967 ◽  
Vol 7 (3) ◽  
pp. 513-516
Author(s):  
V. Statulevičius
Keyword(s):  
Large Deviations ◽  
Random Number ◽  
Random Variables ◽  
Independent Random Variables ◽  
Probabilities Of Large Deviations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: В. А. Статулявичюс. О вероятностях больших уклонений для суммы случайного числа независимых случайных величин V. Statulevičius. Didelių atsilenkimų tikimybių nepriklausomų atsitiktinių dydžių sumai su atsitiktiniu dėmenų skaičiumi klausimu

scholarly journals Theorems on large deviations for the sum of random number of summands

2010 ◽  
Vol 51 ◽  
Author(s):  
Aurelija Kasparavičiūtė ◽  
Leonas Saulis
Keyword(s):  
Large Deviations ◽  
Rate Of Convergence ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Compound Process ◽  
Independent Identically Distributed

In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i = 1, 2, . . . with  mean EXi = µ and variance DXi = σ2 > 0. It is assumed that Nt is a non-negative integervalued random variable, which depends on t > 0 and is independent of Xi, i = 1, 2, . . . .

scholarly journals Normal approximation for sum of random number of summands

2021 ◽  
Vol 47 ◽  
Author(s):  
Leonas Saulis ◽  
Dovilė Deltuvienė
Keyword(s):  
Large Deviations ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Negative Integer

Normal aproximationof sum Zt =ΣNti=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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