On Distributions of Sums of Record Values

Abstract

The lower and upper record values obtained from sequences of independent and identically distributed [0, 1] random variables are discussed in this paper. Representations, in which record values are equal in distribution to sums and products of independent and identically distributed auxiliary random variables, are provided. Using these representations, distributional and moment characteristics of lower and upper record values taken from uniform samples are studied. Sequential sums of lower record values taken from samples of independent and uniformly distributed random variables are also discussed. 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. We also compared the sums of lower order statistics and record values which belong to a certain uniform sample.