Article

Title: Bivariate Limit Theorems for Record Values Based on Random Sample Sizes

Issue: Volume 82 Series A Part 1 Year 2020
Pages: 50 -- 67
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 quasiproducts are obtained. Moreover, the classes of the non-degenerate limit df’s of these statistics are derived.
Primary 60F05, 62E20; Secondary 62E15
Keywords and phrases: Weak convergence, Random sample size, Joint record values, Record functions