Addendum: A Remainder Term Estimate in a Random-Sum Central Limit Theorem

1985 ◽  
Vol 29 (1) ◽  
pp. 199-199
Author(s):  
G. Englund
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Random Sum

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 On the estimation of the remainder term in the multidimensional central limit theorem

1971 ◽  
Vol 11 (4) ◽  
pp. 905-910
Author(s):  
H. Jasiūnas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Multidimensional Central Limit Theorem

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: Г. Ясюнас. Об оценке остаточного члена в многомерной центральной предельной теореме H. Jasiūnas. Liekamoje nario įvertinimas daugiamatėje centrinėje ribinėje teoremoje

scholarly journals On the estimate of the remainder term in the central limit theorem for non-equally distributed random variables

1972 ◽  
Vol 12 (4) ◽  
pp. 183-194
Author(s):  
V. Paulauskas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Random Variables ◽  
The Central Limit Theorem

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. Паулаускас. Оценка скорости сходимости в центральной предельной теореме для разнораспределенных слагаемых V. Paulauskas. Konvergavimo greičio įvertinimas centrinėje ribinėje teoremoje nevienodai pasiskirsčiusiems dėmenims

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.

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