![]() ![]() A variety of complex arithmetic problems can be solved using a single-and fairly simple-approach based on probability bounds analysis. Introduction : Dans cette fiche, nous allons illustrer un schéma de Bernoulli, avec un algorithme simulant une « planche de Galton ». The inputs are first expressed as interval bounds on cumulative distribution functions. Each uncertain input variable is then decomposed into a list of pairs of the form (interval, probability). A Cartesian product of these lists, reflecting both the independence among inputs and the mathematical expression that binds them together, creates another list, which is recomposed to form the resulting uncertain number as upper and lower bounds on a cumulative distribution function. Moment propagation formulas are simultaneously used to bound mean and variance estimates accompanying the bounds on the cumulative distribution function.Īncillary techniques are also employed, such as condensation, which is necessary to keep the length of the list from growing inordinately in sequential operations, and subinterval reconstitution, which is needed to solve interval arithmetic problems involving repeated parameters. Generalizations of this approach are also described that allow for dependencies other than independence, completely unknown dependence, and model uncertainty more generally. Dans la simulation, on a dix rangées de clous et onze. On lache les billes au sommet et celles-ci rebondissent de clou en clou jusquà la base de la planche ou elles sont collectées dans des réservoirs. The present study addresses the analysis of structures with uncertain properties modelled as random variables characterized by imprecise Probability Density Functions (PDFs), namely PDFs with interval basic parameters (mean-value, variance, etc.). La planche de Galton est constituée de rangées hoirizontales de clous décalées dun demi-cran par rapport à la précédente. Due to imprecision in the probabilistic model, the statistics of the response and the failure probability are described by interval quantities. An efficient procedure for evaluating the bounds of such quantities is developed. ![]() The proposed method stems from the application of a ratio of polynomial response surface (Impollonia and Sofi, 2003 Sofi and Romeo, 2018) in conjunction with the classical probabilistic analysis and the so-called Improved Interval Analysis via Extra Unitary Interval (IIA via EUI) (Muscolino and Sofi, 2012). Interval response statistics are derived as approximate explicit functions of the interval parameters describing imprecise probabilities. The range of the interval failure probability is estimated in terms of the interval reliability index once the bounds of the interval mean-value and variance of the response are evaluated. Numerical results concerning a frame structure and a grid structure with uncertain Young’s moduli characterized by imprecise PDFs are presented. Des billes roulent à la surface dune planche inclinée sur laquelle sont disposés des clous en. CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.The accuracy of the proposed method along with the influence of randomness and imprecision of the input parameters on response statistics and reliability assessment are investigated. La planche de Galton, du nom de son inventeur Sir Francis Galton (1822-1911), est un dispositif destiné à visualiser la loi des écarts à la moyenne dans le cadre dune série dun grand nombre dexpériences aléatoires indépendantes. This licensing tag was added to this file as part of the GFDL licensing update. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made.to share – to copy, distribute and transmit the work.This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. GFDL GNU Free Documentation License true true (1998), Simulation of a multitype Galton-Watson chain, Simulation Practice and Theory 6(7), 657-663. A copy of the license is included in the section entitled GNU Free Documentation License. (2010), Relative frequencies and parameter estimation in multi-type Bienayme - Galton - Watson processes, Masters Thesis, Master of Science in Statistics. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. I, the copyright holder of this work, hereby publish it under the following licenses:
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