We obtain strong laws of large numbers for the number of weak records among the first n observations from a sequence of nonnegative integer-valued independent identically distributed random variables.

We study one-dimensional resource sharing systems which can be seen as interacting particle systems taking values in . We first get, by coupling techniques, an estimate of their invariant measures. Then, for processes having a reversible measure, we show the uniqueness of the invariant measure...

In this work we study stochastic comparisons for probabilistic cellular automata where the set of values each automaton can take is an arbitrary finite set endowed with a partial or total order. We give necessary and sufficient conditions on the parameters which define the processes for their...

New inferential procedures for the geometric distribution, based on δ-records, are developed. Maximum likelihood and Bayesian approaches for parameter estimation and prediction of future records are considered. The performance of the estimators is compared with those based solely on...

We prove, under mild conditions, a result about the speed of convergence of a class of estimators found by optimization of certain random criterion functions. We apply the result to the estimator of Least Absolute Deviations (LAD) in a Linear Model without second-order moment assumptions.

Combining data of several tests or markers for the classification of patients according to their health status for assigning better treatments is a major issue in the study of diseases such as cancer. In order to tackle this problem, several approaches have been proposed in the literature. In...

We consider a discrete-time ergodic Markov chain on a partially ordered state space and study the stochastic comparison between its invariant measure and some measures related with the behaviour of the chain conditioned to avoid a decreasing subset of the state space. We also study the situation...