scholarly journals Limit theorems for the diameter of a random sample in the unit ball

Extremes ◽  
2007 ◽  
Vol 10 (3) ◽  
pp. 129-150 ◽  
Author(s):  
Michael Mayer ◽  
Ilya Molchanov
Keyword(s):  
Unit Ball ◽  
Random Sample ◽  
Limit Theorems

Limit theorems for extremes with random sample size

1998 ◽  
Vol 30 (03) ◽  
pp. 777-806 ◽  
Author(s):  
Dmitrii S. Silvestrov ◽  
Jozef L. Teugels
Keyword(s):  
Weak Convergence ◽  
Sample Size ◽  
Random Sample ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Random Sample Size ◽  
Extremal Processes ◽  
Convergence Type

This paper is devoted to the investigation of limit theorems for extremes with random sample size under general dependence-independence conditions for samples and random sample size indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems for extremal processes with random sample size indexes.

Bivariate Limit Theorems for Record Values Based on Random Sample Sizes

Sankhya A ◽  
2019 ◽  
Vol 82 (1) ◽  
pp. 50-67
Author(s):  
M. A. Abd Elgawad ◽  
H. M. Barakat ◽  
Ting Yan
Keyword(s):  
Random Sample ◽  
Limit Theorems ◽  
Record Values ◽  
Sample Sizes

On maximum family size in branching processes

1999 ◽  
Vol 36 (3) ◽  
pp. 632-643 ◽  
Author(s):  
Ibrahim Rahimov ◽  
George P. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Sample Size ◽  
Random Sample ◽  
Family Size ◽  
Limit Theorems ◽  
Branching Processes ◽  
Random Sample Size ◽  
Convergence Results ◽  
Watson Process ◽  
Supercritical Branching Processes

The number Yn of offspring of the most prolific individual in the nth generation of a Bienaymé–Galton–Watson process is studied. The asymptotic behaviour of Yn as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Yn and EYn provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.

On maximum family size in branching processes

1999 ◽  
Vol 36 (03) ◽  
pp. 632-643 ◽  
Author(s):  
Ibrahim Rahimov ◽  
George P. Yanev
Keyword(s):  
Asymptotic Behaviour ◽  
Sample Size ◽  
Random Sample ◽  
Family Size ◽  
Limit Theorems ◽  
Branching Processes ◽  
Random Sample Size ◽  
Convergence Results ◽  
Watson Process ◽  
Supercritical Branching Processes

The number Y n of offspring of the most prolific individual in the nth generation of a Bienaymé–Galton–Watson process is studied. The asymptotic behaviour of Y n as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Y n and EY n provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.

Limit theorems for extremes with random sample size

1998 ◽  
Vol 30 (3) ◽  
pp. 777-806 ◽  
Author(s):  
Dmitrii S. Silvestrov ◽  
Jozef L. Teugels
Keyword(s):  
Weak Convergence ◽  
Sample Size ◽  
Random Sample ◽  
Limit Theorems ◽  
Functional Limit ◽  
Functional Limit Theorems ◽  
Random Sample Size ◽  
Extremal Processes ◽  
Convergence Type

This paper is devoted to the investigation of limit theorems for extremes with random sample size under general dependence-independence conditions for samples and random sample size indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems for extremal processes with random sample size indexes.

Limit theorems for statistics with random sample sizes

2015 ◽  
Author(s):  
M. E. Grigoryeva ◽  
Victor Yu. Korolev ◽  
Alexander I. Zeifman
Keyword(s):  
Random Sample ◽  
Limit Theorems ◽  
Sample Sizes

scholarly journals Limit Theorems for Bivariate Generalised Order Statistics in Stationary Gaussian Sequences with Random Sample Sizes

2019 ◽  
Vol 73 (6) ◽  
pp. 525-532
Author(s):  
Fatma Hashem Essawe ◽  
Mohamed Abd Elgawad ◽  
Haroon Mohamed Barakat ◽  
Hui Zhao
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Random Sample ◽  
Limit Theorems ◽  
Sufficient Conditions ◽  
Distribution Functions ◽  
Random Sample Size ◽  
Lower Upper ◽  
Set Up ◽  
Random Indices

Abstract In this paper, we study the limit distribution functions of the (lower-lower), (upper-upper) and (lower-upper) extreme and central-central m-generalised order statistics (m–GOS) of stationary Gaussian sequences under an equi-correlated set up, when the random sample size is assumed to converge weakly and independent of the basic variables. Moreover, sufficient conditions for a weak convergence of generalised quasi-range with random indices are obtained.

Limit theorems and price changes in financial markets

1998 ◽  
Vol 77 (5) ◽  
pp. 1353-1356
Author(s):  
Rosario N. Mantegna, H. Eugene Stanley
Keyword(s):  
Financial Markets ◽  
Limit Theorems ◽  
Price Changes
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