The Esseen inequality for sums of a random number of differently distributed random variables

1977 ◽  
Vol 22 (1) ◽  
pp. 569-571 ◽  
Author(s):  
Kh. Batirov ◽  
D. V. Manevich ◽  
S. V. Nagaev
Keyword(s):  
Random Number ◽  
Random Variables ◽  
Esseen Inequality ◽  
Inequality For Sums

Berry-esseen inequality for the sum of a random number of independent random variables

1980 ◽  
Vol 28 (2) ◽  
pp. 616-617
Author(s):  
Z. Rychlik
Keyword(s):  
Random Number ◽  
Random Variables ◽  
Independent Random Variables ◽  
Esseen Inequality

scholarly journals The Markov Inequality for Sums of Independent Random Variables

1969 ◽  
Vol 40 (6) ◽  
pp. 1980-1984 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Markov Inequality ◽  
Inequality For Sums

scholarly journals A conditional Berry–Esseen inequality

2019 ◽  
Vol 56 (01) ◽  
pp. 76-90
Author(s):  
Thierry Klein ◽  
Agnés Lagnoux ◽  
Pierre Petit
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Esseen Inequality ◽  
Independent And Identically Distributed

AbstractAs an extension of a central limit theorem established by Svante Janson, we prove a Berry–Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.

The distribution of the maximum of a random number of random variables with applications

1973 ◽  
Vol 10 (01) ◽  
pp. 122-129 ◽  
Author(s):  
Janos Galambos
Keyword(s):  
Service Time ◽  
Joint Distribution ◽  
Random Number ◽  
Random Variables ◽  
Stochastic Independence ◽  
Fixed Integer ◽  
Number Of Components ◽  
Distribution Of The Maximum ◽  
Distribution Of Elements ◽  
Mild Assumption

The asymptotic distribution of the maximum of a random number of random variables taken from the model below is shown to be the same as when their number is a fixed integer. Applications are indicated to determine the service time of a system of a large number of components, when the number of components to be serviced is not known in advance. A much slighter assumption is made than the stochastic independence of the periods of time needed for servicing the different components. In our model we assume that the random variables can be grouped into a number of subcollections with the following properties: (i) the random variables taken from different groups are asymptotically independent, (ii) the largest number of elements in a subgroup is of smaller order than the overall number of random variables. In addition, a very mild assumption is made for the joint distribution of elements from the same group.

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