The limit theorems on extreme order statistics and partial sums of i.i.d. random variables-Reference-Cited by-同舟云学术

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The limit theorems on extreme order statistics and partial sums of i.i.d. random variables

Published:2024-01-01 Issue:1 Volume:22 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Li Gaoyu¹²,Ling Chengxiu³,Tan Zhongquan²

Affiliation:

1. School of Mathematic Sciences, Zhejiang Normal University , Jinhua 321004 , P. R. China

2. College of Data Science, Jiaxing University , Jiaxing 314001 , P. R. China

3. Academy of Pharmacy, Xi’an Jiaotong-Liverpool University , Suzhou , 215123 , P. R. China

Abstract

Abstract This article proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/math-2024-0047/pdf

Reference31 articles.

1. T. L. Chow and J. L. Teugels, The sum and the maximum of i.i.d. random variables, Proceedings on 2nd Prague Symposium on Asymptotic Statistics (Hradec Králové, 1978), 1979, pp. 81–92.

2. M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983.

3. P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events, Springer, Berlin, 1997.

4. L. de Haan and H. Ferreira, Extreme Value Theory, Springer, New York, 2006.

5. C. W. Anderson and K. F. Turkman, The joint limiting distribution of sums and maxima of stationary sequences, J. Appl. Probab. 28 (1991), no. 1, 33–44, DOI: https://doi.org/10.2307/3214738.

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