Bivariate Limit Theorems for Record Values Based on Random Sample Sizes

M. A. Abd Elgawad (), H. M. Barakat and Ting Yan
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M. A. Abd Elgawad: Wuhan University of Technology
H. M. Barakat: Zagazig University
Ting Yan: Central China Normal University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 1, No 4, 50-67

Abstract: Abstract In this paper, the class of limit distribution functions (df’s) of the joint upper record values with random sample size is fully characterized. Necessary and sufficient conditions, as well as the domains of attraction of the limit df’s are obtained. As an application of this result, the sufficient conditions for the weak convergence of the random of record quasi-ranges, record quasi-midranges, record extremal quasi-quotients and record extremal quasi-products are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.

Keywords: Weak convergence; Random sample size; Joint record values; Record functions; Primary 60F05; 62E20; Secondary 62E15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13171-019-00167-2

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