Monotone runs of uniformly distributed integer random variables: A probabilistic analysis

Monotone runs of uniformly distributed integer random variables: A probabilistic analysis

Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Alternating Runs of Geometrically Distributed Random Variables

Run statistics about a sequence of independent geometrically distributed random variables has attracted some attention recently in many areas such as applied probability, reliability, statistical process control, and computer science. In this paper, we first study the mean and variance of the number of alternating runs in a sequence of independent geometrically distributed random variables. The...

Ascending runs in dependent uniformly distributed random variables: Application to wireless networks

We analyze in this paper the longest increasing contiguous sequence or maximal ascending run of random variables with common uniform distribution but not independent. Their dependence is characterized by the fact that two successive random variables cannot take the same value. Using a Markov chain approach, we study the distribution of the maximal ascending run and we develop an algorithm to co...

Random variables, monotone relations, and convex analysis

Random variables can be described by their cumulative distribution functions, a class of nondecreasing functions on the real line. Those functions can in turn be identified, after the possible vertical gaps in their graphs are filled in, with maximal monotone relations. Such relations are known to be the subdifferentials of convex functions. Analysis of these connections yields new insights. Th...