A generalization of the Esseen inequality for the concentration function

1987 ◽  
Vol 36 (4) ◽  
pp. 473-476 ◽  
Author(s):  
A. I. Daugavet ◽  
V. V. Petrov
Keyword(s):  
Concentration Function ◽  
Esseen Inequality

A Multidimensional Analogue of the Berry-Esseen Inequality for Sets with Bounded Diameter

1966 ◽  
Vol 11 (3) ◽  
pp. 447-454 ◽  
Author(s):  
V. M. Zolotarev
Keyword(s):  
Multidimensional Analogue ◽  
Esseen Inequality

Continuity for multi-type branching processes with varying environments

1999 ◽  
Vol 36 (01) ◽  
pp. 139-145 ◽  
Author(s):  
Owen Dafydd Jones
Keyword(s):  
Linear Combination ◽  
Branching Process ◽  
Branching Processes ◽  
Random Variables ◽  
Main Tool ◽  
Concentration Function ◽  
Independent Random Variables ◽  
Varying Environments

Conditions are derived for the components of the normed limit of a multi-type branching process with varying environments, to be continuous on (0, ∞). The main tool is an inequality for the concentration function of sums of independent random variables, due originally to Petrov. Using this, we show that if there is a discontinuity present, then a particular linear combination of the population types must converge to a non-random constant (Equation (1)). Ensuring this can not happen provides the desired continuity conditions.

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 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

scholarly journals On the definition of a concentration function relevant to the ROC curve

METRON ◽  
2020 ◽  
Vol 78 (3) ◽  
pp. 271-277
Author(s):  
Mauro Gasparini ◽  
Lidia Sacchetto
Keyword(s):  
Roc Curve ◽  
Population Level ◽  
Concentration Function ◽  
Concentration Curve ◽  
Classification Problems ◽  
The One ◽  
Definition Of ◽  
The Relationship

AbstractThis work provides a definition of concentration curve alternative to the one presented on this journal by Schechtman and Schechtman (Metron 77:171–178, 2019). Our definition clarifies, at the population level, the relationship between concentration and the omnipresent ROC curve in diagnostic and classification problems.

On the Concentration Function

1978 ◽  
Vol 22 (2) ◽  
pp. 362-366 ◽  
Author(s):  
L. P. Postnikova ◽  
A. A. Yudin
Keyword(s):  
Concentration Function

On computing the constant in the berry-esseen inequality for a class of distributions

1993 ◽  
Vol 32 (4) ◽  
pp. 410-413
Author(s):  
A. Mitalauskas
Keyword(s):  
Esseen Inequality
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