20 / 12 / 2022 - 14:00 – 14:30

Haron M. Barakat

Faculty of Science, Zaqazig University

Asymptotic Behavior of Ordered Statistics and Record Values in a Mixture of Two Gaussian Sequences

Abstract

In this talk, we investigate the limit distributions of extreme, intermediate, and central order statistics, as well as record values, of a mixture of two stationary Gaussian sequences under an equi-correlated setup. Moreover, when the random sample size is assumed to converge weakly and to be independent of the basic variables, the asymptotic distributions of that statistics are derived. 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.