On Distribution of Upper Marginal Records in Bivariate Random Sequences

Abstract

The theory of record values has been extensively studied in the statistical literature. However, there are not many papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents the marginal record values and record times in extended sequence of bivariate random vectors. The joint distributions of some upper marginal records are derived. Some results on joint probability mass function of upper record time vectors and distribution function of upper record value vectors are given via copula functions. Moreover, the numerical and graphical applications of considered upper records using flood data and prediction of rainfall variables such as intensity, depth, and duration are provided.