scholarly journals A CENTRAL LIMIT THEOREM FOR GENERAL WEIGHTED SUM OF LNQD RANDOM VARIABLES AND ITS APPLICATION

2005 ◽  
Vol 20 (3) ◽  
pp. 531-538 ◽  
Author(s):  
HYUN-CHULL KIM ◽  
TAE-SUNG KIM
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Weighted Sum

scholarly journals Remainder term estimates in a conditional central limit theorem for integer-valued random variables

1985 ◽  
Vol 39 (1) ◽  
pp. 75-85 ◽  
Author(s):  
M. P. Quine
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Conditional Distribution ◽  
Finite Population ◽  
Random Variables ◽  
Weighted Sum ◽  
Type Result ◽  
Conditional Central Limit Theorem

AbstractA Berry-Esseen type result is given for the conditional distribution of a weighted sum of i.i.d. integer-valued r.v.'s given that their unweighted sum equals its expectation. The examples include the case of sampling without replacement from a finite population.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

scholarly journals A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables

2021 ◽  
Vol 499 (1) ◽  
pp. 124982
Author(s):  
Benjamin Avanzi ◽  
Guillaume Boglioni Beaulieu ◽  
Pierre Lafaye de Micheaux ◽  
Frédéric Ouimet ◽  
Bernard Wong
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Independent Identically Distributed

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

scholarly journals A Central Limit Theorem and its Applications to Multicolor Randomly Reinforced Urns

2011 ◽  
Vol 48 (02) ◽  
pp. 527-546 ◽  
Author(s):  
Patrizia Berti ◽  
Irene Crimaldi ◽  
Luca Pratelli ◽  
Pietro Rigo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Bayesian Statistics ◽  
Central Limit ◽  
Random Variables

Let X n be a sequence of integrable real random variables, adapted to a filtration (G n ). Define C n = √{(1 / n)∑ k=1 n X k − E(X n+1 | G n )} and D n = √n{E(X n+1 | G n ) − Z}, where Z is the almost-sure limit of E(X n+1 | G n ) (assumed to exist). Conditions for (C n , D n ) → N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain √n{(1 / n)∑ k=1 n X_k - Z} = C n + D n → N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns.

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