Search results for "Random variable"

Repetition times for Gibbsian sources

1999

In this paper we consider the class of stochastic stationary sources induced by one-dimensional Gibbs states, with Holder continuous potentials. We show that the time elapsed before the source repeats its first n symbols, when suitably renormalized, converges in law either to a log-normal distribution or to a finite mixture of exponential random variables. In the first case we also prove a large deviation result.

Fuzzy Logic for Medical Engineering: An Application to Vessel Segmentation

2007

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

2020

A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time t the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at x &isin

On the fractional probabilistic Taylor's and mean value theorems

2016

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…

Bartlett formalism generating functions and Z-transforms in fluctuation and noise theory

1983

Abstract “La theorie des fonctions generatrices s'adapte elle meme et avec la plus grande generalite aux questions des probabilite les plus difficiles.” (Laplace, 1812) “An important part of probability theory consists of the derivation of the probability distribution of the sum of n random variables, each of which obeys a given probability law, and the development of asymptotic forms of these distributions valid for increasing n. Probability generating functions owe their dominant position to the simplification they permit to both problems. Their employment to obtain the successive moments of a probability distribution and to solve the difference equations of probability theory is ancillar…

Reliability Analysis of a Controlled Stage-Constructed and Reinforced Embankment on Soft Ground Using 2D and 3D Models

2020

Geosynthetic reinforcement has become a very practical technique to improve geotechnical structure safety. In spite of improved soil behavior, structures are affected by uncertainties related to soil and reinforcement material properties. This paper aims to present a reliability analysis in order to take statistical information (uncertainties) into account in a safety analysis of reinforced embankments. The analysis was used in a case study on a controlled stage-constructed embankment on soft ground in order to investigate its probabilistic stability. Modeling was performed by commercial geotechnical software usage (GeoStudio and RocScience packs, SIGMA/W+SLOPE/W and SLIDE³, respectively) a…

Exact simulation of first exit times for one-dimensional diffusion processes

2019

International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …

Path integral solution by fractional calculus

2008

In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.

Accounting for soil parameter uncertainty in a physically based and distributed approach for rainfall-triggered landslides

2015

In this study we propose a probabilistic approach for coupled distributed hydrological-hillslope stability models that accounts for soil parameters uncertainty at basin scale. The geotechnical and soil retention curve parameters are treated as random variables across the basin and theoretical probability distributions of the Factor of Safety (FS) are estimated. The derived distributions are used to obtain the spatio-temporal dynamics of probability of failure, in terms of parameters uncertainty, conditioned to soil moisture dynamics. The framework has been implemented in the tRIBS-VEGGIE (Triangulated Irregular Network (TIN)-based Real-time Integrated Basin Simulator-VEGetation Generator fo…

Fast equivariant JADE

2013

Independent component analysis (ICA) is a widely used signal processing tool having applications in various fields of science. In this paper we focus on affine equivariant ICA methods. Two such well-established estimation methods, FOBI and JADE, diagonalize certain fourth order cumulant matrices to extract the independent components. FOBI uses one cumulant matrix only, and is therefore computationally very fast. However, it is not able to separate identically distributed components which is a major drawback. JADE overcomes this restriction. Unfortunately, JADE uses a huge number of cumulant matrices and is computationally very heavy in high-dimensional cases. In this paper, we hybridize the…