ASYMPTOTIC BEHAVIOR OF THE RECORD VALUES IN A STATIONARY GAUSSIAN SEQUENCE, WITH APPLICATIONS

被引：5

作者：

Barakat, Haroon M. ^{[1
]}

Abd Elgawad, M. A. ^{[2
,3
]}

机构：

[1] Zagazig Univ, Dept Math, Fac Sci, Zagazig 44519, Egypt

[2] Wuhan Univ Technol, Sch Comp Sci & Technol, Wuhan 430070, Hubei, Peoples R China

[3] Benha Univ, Dept Math, Fac Sci, Banha 13518, Egypt

来源：

MATHEMATICA SLOVACA | 2019年 / 69卷 / 03期

关键词：

weak convergence; record values; joint record values; record functions; LIMIT DISTRIBUTIONS; ORDER-STATISTICS;

D O I：

10.1515/ms-2017-0259

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the limit distributions of upper and lower record values of a stationary Gaussian sequence under an equi-correlated set up. Moreover, the class of limit distribution functions (df's) of the joint upper (and the lower) record values of a stationary Gaussian sequence is fully characterized. As an application of this result, the sufficient conditions for the weak convergence of the record quasi-range, record quasi-mid-range, record extremal quasi-quotient and record extremal quasi-product are obtained. Moreover, the classes of the non-degenerate limit df's of these statistics are derived.

引用

页码：707 / 720

页数：14

共 50 条

[11] THE ASYMPTOTIC-BEHAVIOR OF EXTREME VALUES OF STATIONARY-SEQUENCES
OBRIEN, GL
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1985, 19 (01) : 52 - 52
[12] The asymptotic behavior of the singular values of matrix powers and applications
Faculteit Wiskunde en Informatica, Vrije Universiteit, Amsterdam, Netherlands
Linear Algebra and Its Applications, 1996, 245 : 55 - 76
[13] AN ASYMPTOTIC PROPERTY OF GAUSSIAN STATIONARY PROCESSES
WATANABE, H
PROCEEDINGS OF THE JAPAN ACADEMY, 1968, 44 (09): : 895 - &
[14] The asymptotic behavior of the singular values of matrix powers and applications
Gohberg, I
Kaashoek, MA
Kos, J
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 245 : 55 - 76
[15] Asymptotic behavior of the singular values of matrix powers and applications
Gohberg, I.
Kaashoek, M.A.
Kos, J.
Linear Algebra and Its Applications, 1996, 245
[16] Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence
Tan Zhong-quan
Peng Zuo-xiang
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2011, 26 (03) : 319 - 326
[17] Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence
Zhong-quan Tan
Zuo-xiang Peng
Applied Mathematics-A Journal of Chinese Universities, 2011, 26 : 319 - 326
[18] Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence
TAN Zhong-quan 1
Applied Mathematics:A Journal of Chinese Universities, 2011, (03) : 319 - 326
[19] Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence
TAN Zhongquan PENG Zuoxiang Department of MathematicsZunyi Normal CollegeZunyi China Department of MathematicsSoochow UniversitySuzhou China School of Mathematics and StatisticsSouthwest UniversityChongqing China
Applied Mathematics:A Journal of Chinese Universities(Series B), 2011, 26 (03) : 319 - 326
[20] THE ASYMPTOTIC DEPENDENCE STRUCTURE AND SOME FUNCTIONS OF GENERALIZED ORDER STATISTICS IN A STATIONARY GAUSSIAN SEQUENCE
Barakat, Haroon M.
MATHEMATICAL REPORTS, 2021, 23 (04): : 437 - 451

← 1 2 3 4 5 →