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 notmany papers devoted to the theory of records for bivariate and multivariate random sequences. This paper presents themarginal record values and record times in extended sequence of bivariate random vectors. The joint distributions ofsome upper marginal records are derived. Some results on joint probability mass function of upper record time vectorsand distribution function of upper record value vectors are given via copula functions. Moreover, the numerical andgraphical applications of considered upper records using flood data and prediction of rainfall variables such as intensity,depth, and duration are provided.