Ascending runs of sequences of geometrically distributed 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...

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

D-records in Geometrically Distributed Random Variables

We study d–records in sequences generated by independent geometric random variables and derive explicit and asymptotic formulæ for expectation and variance. Informally speaking, a d–record occurs, when one computes the d–largest values, and the variable maintaining it changes its value while the sequence is scanned from left to right. This is done for the “strict model,” but a “weak model” is a...

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...