Search

We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted residual entropy" and "weighted past entropy", that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively. The obtained results include their behaviors under monotonic transformations., Comment: 13 pages; updated on June 21, 2011

Viene offerta una sintesi di argomenti del calcolo delle probabilità e della teoria dei processi stocastici svolti nell'ambito di corsi tenuti da uno degli autori sin dagli inizi degli anni '80. La costruzione assiomatica della probabilità viene esposta facendo ricorso alla nozione di successioni di eventi, ed un capitolo è dedicato alle funzioni caratteristiche utilizzate per la dimostrazione della legge debole dei grandi numeri e del teorema centrale del limite. Si espongono, infine, gli elementi della teoria dei processi stocastici di diffusione. Il volume, rivolto agli studenti dei nuovi ordinamenti dei corsi di studio afferenti alle facoltà di scienze, ingegneria ed economia, costituisce utile strumento di consultazione anche per operatori in aree disciplinari quali sociologia e medicina.

A vector algorithm is provided for simulating stochastic stationary normal processes with rational spectral densities, in order to determine first-crossing-time densities for the general case of time-varying boundaries. The results of massive simulations are discussed and conclusions are drawn on the effects of boundaries and covariances oscillations on determining qualitative and quantitative features of the densities. The observed shapes are seen to depend not only on the forms of the boundaries but also on the specific numerical values of the parameters of the processes. Indeed, they turn out to be unimodal, bimodal or multimodal even for fixed shapes of the covariance functions and of the boundaries. This is unexpectedly different from the case of diffusion processes whose first-crossing-time densities are either unimodal, or rigorously multimodal in the case of periodic boundaries. Such a feature makes normal processes particular suitable for modeling purposes.

Parrondo's paradox arises in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. We present a suitable version of Parrondo's paradox in reliability theory involving two systems in series, the units of the first system being less reliable than those of the second. If the first system is modified so that the distributions of its new units are mixtures of the previous distributions with equal probabilities, then under suitable conditions the new system is shown to be more reliable than the second in the "usual stochastic order" sense., 6 pages

We consider the first-crossing-time problem through a constant boundary for a Wiener process perturbed by random jumps driven by a counting process. On the base of a sample-path analysis of the jump-diffusion process we obtain explicit lower bounds for the first-crossing-time density and for the first-crossing-time distribution function. In the case of the distribution function, the bound is improved by use of processes comparison based on the usual stochastic order. The special case of constant jumps driven by a Poisson process is thoroughly discussed., 12 pages, 4 figures

We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided., 14 pages, 6 figures