Оn the distributions of sums of record values

Abstract

In the present paper, we discuss lower and upper record values obtained from sequences of independent and identically distributed on [0,1] random variables. Representations, in which such record values are equal in distribution to sums and products of independent and identically distributed auxiliary random variables, are provided in the paper. By these representations distributional and moment characteristics of lower and upper record values taken from uniform samples are studied. Sequential sums of lower record values which are taken from samples of independent and uniformly distributed random variables are also discussed in this work. The distributions and the Laplace transforms of the given sums are studied. The Laplace transform of the series of lower uniform record values are found. In the present work, we also compare the sums of lower order statistics and record values which belong to a certain uniform sample.