Multivariate records based on dominance. (English) Zbl 1225.60043

Summary: We consider three types of multivariate records in this paper and derive the mean and the variance of their numbers for independent and uniform random samples from two prototype regions: the hypercube \([0,1]^d\) and the \(d\)-dimensional simplex. Central limit theorems with convergence rates are established when the variance tends to infinity. Effective numerical procedures are also provided for computing the variance constants to a high degree of precision.


60F05 Central limit and other weak theorems
60C05 Combinatorial probability
60G70 Extreme value theory; extremal stochastic processes
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