On the Record Range

Ramin Kazemi

Abstract

In this paper we consider some distributional properties of record range of a sequence of i.i.d continuous uniform random variables. More precisely, We calculate the entropy of the record range and evaluate it as function of $n$. Also we calculate the joint probability density function of $R_n$ and $R_m$ via  a Markov chain and show that the conditional density of $R_n$ given $R_{n-1}$ is independent of $n$. Finally, We  prove some nice equalities related to the moments of the record range.