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L'analyse implicative bayésienne, une méthode pour l'étude des dépendances orientées. II : modèle logique sur un tableau de contingence

Jean-Marc Bernard, Camilo Charron (1996)

Mathématiques et Sciences Humaines

Dans Bernard & Charron (1996), nous avons proposé une nouvelle méthode, l'Analyse Implicative Bayésienne (AIB), pour l'étude des dépendances orientées entre deux variables binaires, méthode qui permet de conclure en terme de quasi-implication entre modalités des variables. Nous étendons ici cette méthode au cas d'un tableau de contingence A × B quelconque avec le problème de la mesure du degré de quasi-adéquation des données à un modèle logique donné. Au niveau descriptif, la méthode repose...

L'analyse implicative bayésienne, une méthode pour l'étude des dépendances orientées. I : données binaires

Jean-Marc Bernard, Camilo Charron (1996)

Mathématiques et Sciences Humaines

La réussite à l'épreuve A implique-t-elle, approximativement, la réussite à l'épreuve B ? Parmi les indices descriptifs proposés pour mesurer de telles dépendances orientées, nous considérons l'indice H de Loevinger, qui s'exprime simplement en termes des taux de liaison entre modalités. A partir de cet indice, nous définissons les notions de quasi-implication, de quasi-équivalence et de quasi-indépendance dans un tableau de contingence 2 x 2. Cependant, les méthodes inductives correspondantes,...

Laplace-Stieltjes transform of the system mean lifetime via geometric process model

Gökhan Gökdere, Mehmet Gürcan (2016)

Open Mathematics

Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a...

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

Mokkadem, Abdelkader, Mariane, Pelletier, Baba, Thiam (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 62G07, 60F10.In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the uniform deviations.

Large deviations for quasi-arithmetically self-normalized random variables

Jean-Marie Aubry, Marguerite Zani (2013)

ESAIM: Probability and Statistics

We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means, we generalize the large deviation result on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. Ann. Probab. 25 (1997) 285–328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.

Large losses-probability minimizing approach

Michał Baran (2004)

Applicationes Mathematicae

The probability minimizing problem for large losses of portfolio in discrete and continuous time models is studied. This gives a generalization of quantile hedging presented in [3].

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