Distributions and moments of record values in a sequence of maximally dependent random variables

A sequence of possibly dependent random variables is maximally dependent if all the sample maxima in the sequence have stochastically maximal distributions in the class of all distributions with the same marginals. For a sequence of maximally dependent standard uniform random variables, we determine the distribution functions of record times and values. We show that the distribution of the record occurrence times coincides with the respective distribution for the i.i.d. sequence, and the distributions of the record values are stochastically maximal in the class of sequences with the same record times distributions, containing all the exchangeable sequences. We also derive analytic formulae for the moments of record values from the maximally dependent sequence, and compare them with those of the i.i.d. case.