1,720,983 research outputs found
Esercizi di statistica per l'ingegneria, le scienze e l'economia
No full textQuesto libro attinge dalla grande quantita di esercizi di statistica che gli autori hanno formulato per lezioni, esercitazioni e prove d’esame negli anni di insegnamento nei Corsi di Studio in Ingegneria al Politecnico di Milano. Il suo obiettivo e’ guidare gli studenti ad applicare le metodologie presentate in corsi introduttivi di statistica, partendo dalla consapevolezza che essi spesso incontrano una grande difficoltà nel passare dalla “teoria” alla “soluzione di problemi”. Il libro presenta un percorso, sviluppato attraverso la proposta di problemi, che aiuti lo studente ad impossessarsi delle tecniche statistiche basilari per problemi inerenti a fenomeni casuali nell’ambito dell’ingegneria, delle scienze e dell’economia
Infinite energy solutions to inelastic homogeneous Boltzmann equation.
Full text linkThis paper is concerned with the existence, shape and dynamical stability of infinite energy equilibria for a class of spatially homogeneous kinetic equations in space dimensions d ≥ 2. Our results cover in particular Bobylev’s model for inelastic Maxwell molecules. First, we show under certain conditions on the collision kernel, that there exists an index α ∈ (0, 2) such that the equation possesses a nontrivial stationary solution, which is a scale mixture of radially symmetric α-stable laws. We also characterize the mixing distribution as the fixed point of a smoothing transformation. Second, we prove that any transient solution that emerges from the NDA of some (not necessarily radial symmetric) α-stable distribution converges to an equilibrium. The key element of the convergence proof is an application of the central limit theorem to a representation of the transient solution as a weighted sum of projections of randomly rotated i.i.d. random vectors
Diffusion approximation for a pseudo-likelihood test process with application to detection of change in a stochastic system
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Propriété asymptotique d'un modèle statistique pour une chaîne de Markov à valeurs dans <em>R<sup>d</sup></em>
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Cox Markov models for estimating single cell growth
Full text linkRecent experimental techniques produce thousands of data of single cell growth, consequently stochastic models of growth can be validated on true data and used to understand the main mechanisms that control the cell cycle. A sequence of growing cells is usually modeled by a suitable Markov chain. In this framework, the most interesting goal is to infer the distribution of the doubling time (or of the added size) of a cell given its initial size and its elongation rate. In the literature, these distributions are described in terms of the corresponding conditional hazard function, referred as division hazard rate. In this work we propose a simple but effective way to estimate the division hazard by using extended Cox modeling. We investigate the convergence to the stationary distribution of the Markov chain describing the sequence of growing cells and we prove that, under reasonable conditions, the proposed estimators of the division hazard rates are asymptotically consistent. Finally, we apply our model to study some published datasets of E-Coli cells
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