Asymptotic behavior of ordered random variables in mixture of two Gaussian sequences with random index

AIMS Mathematics

article

H. M. Barakat¹  M. H. Dwes² 

[1] Department of Mathematics, Faculty of Science, Zagazig University;Department of Mathematics, Faculty of Science, Alexandria University

关键词: mixture distribution;    Gaussian sequences;    random index;    order statistics;    record values;   

DOI  :  10.3934/math.20221060

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

When the random sample size is assumed to converge weakly and to be independent of the basic variables, the asymptotic distributions of extreme, intermediate, and central order statistics, as well as record values, for a mixture of two stationary Gaussian sequences under an equi-correlated setup are derived. Furthermore, sufficient conditions for convergence are derived in each case. An interesting fact is revealed that in several cases, the limit distributions of the aforementioned statistics are the same when the sample size is random and non-random. e.g., when one mixture component has a correlation that converges to a non-zero value.

【 授权许可】

CC BY