Estimation of bivariate excess probabilities for elliptical models

Let $(X,Y)$ be a random vector whose conditional excess probability $\theta(x,y):=P(Y\leq y | X>x)$ is of interest. Estimating this kind of probability is a delicate problem as soon as $x$ tends to be large, since the conditioning event becomes an extreme set. Assume that $(X,Y)$ is elliptically distributed, with a rapidly varying radial component. In this paper, three statistical procedures are proposed to estimate $\theta(x,y)$ for fixed $x,y$, with $x$ large. They respectively make use of an approximation result of Abdous et al. (cf. Canad. J. Statist. 33 (2005) 317--334, Theorem 1), a new second order refinement of Abdous et al.'s Theorem 1, and a non-approximating method. The estimation of the conditional quantile function $\theta(x,\cdot)^{\leftarrow}$ for large fixed $x$ is also addressed and these methods are compared via simulations. An illustration in the financial context is also given.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ140 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A Supply Chain Equilibrium Model with General Price-Dependent Demand

The concept of supply chain equilibrium has been widely employed to solve real-life cases. Under this concept, decisions makers move simultaneously and compete in a noncooperative manner to achieve a supply chain network equilibrium. This paper proposes a supply chain network equilibrium model consisting of multiple raw material suppliers, manufacturers and retailers. Unlike previous studies, we assume that the demand for the product at each retail outlet is modeled as general stochastic functions of price that encompass additive-multiplicative demand models used in previous studies. Under general price-dependent demand functions, we derive the optimality conditions of suppliers, manufacturers and retailers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. The existence and uniqueness of the solution to the variational inequality are examined. A sensitivity analysis and a series of numerical tests are conducted to illustrate the analytical effects of demand distribution, model parameters, demand level and variability on quantity shipments, prices, and expected profits. Managerial insights are reported to show the impact of different types of demand functions and model parameters on the equilibrium solutions

Dual sourcing inventory management with nonconsecutive lead times from a supply chain perspective: a numerical study

We study a stochastic multi-period two-echelon dual sourcing inventory system where the buyer can source a product from two different suppliers: a regular and an expedited supplier. The regular supplier is a low-cost offshore supplier, whereas the expedited supplier is a responsive nearshore supplier. Such dual sourcing inventory systems have been well studied in the literature, mostly being solely evaluated from the buyer’s perspective. Since the buyer’s decisions have an impact on the supply chain profit, we adopt the perspective of the entire supply chain, i.e., by taking the suppliers explicitly into consideration. In addition, we study this system for general (nonconsecutive) lead times for which the optimal policy is unknown or very complex. We numerically compare the performance of two different policies in a two-echelon setting: the Dual-Index Policy (DIP) and the Tailored Base-Surge Policy (TBS). From earlier studies we know that when the lead time difference is one period, DIP is optimal from the buyer’s perspective, but not necessarily from the supply chain perspective. On the other hand, when the lead time difference grows to infinity, TBS becomes optimal for the buyer. In this paper, we evaluate the policies numerically (under various conditions) and we show that from a supply chain perspective, TBS typically outperforms DIP at a limited lead time difference of a few time periods. Based on data collected from 51 manufacturing firms, the results of our paper imply for many supply chains with a dual sourcing setting that TBS quickly becomes a beneficial policy alternative, especially given its simple and appealing structure

A Nonparametric Test of Serial Independence for Time Series and Residuals

AbstractThis paper presents nonparametric tests of independence that can be used to test the independence of p random variables, serial independence for time series, or residuals data. These tests are shown to generalize the classical portmanteau statistics. Applications to both time series and regression residuals are discussed

Conception et fabrication d'un prototype de nez électronique basé sur un système d'apprentissage et de reconnaissance évolutif des composants organiques volatiles

Plusieurs actions sont faites par l’être humain sur la base de la perception d’odeur comme sortir les ordures, changer les couches de bébé, prendre de mesures de la sécurité en cas de fuite de gaz, etc. Mais, le sens d’odorat de l’homme est limité, car il y a des gaz qui sont très toxiques et l’être humain ne peut pas les détecter par le nez comme le monoxyde de carbone. Ainsi, le sens d’odeur est utilisé dans plusieurs applications industrielles dans la production (industries des parfums) ou bien dans la sécurité (industrie de pétrole et du gaz), des applications médicales (détection de bactéries) et des applications de sécurité nationale (détection de cannabis). Depuis plusieurs décennies, la communauté des capteurs essaie de reproduire artificiellement la capacité de l’odorat. La première apparition de nez électroniques ou nez artificiel a été dans les années 1980. Cet appareil est un ensemble de capteurs de gaz et de techniques d’apprentissage et de reconnaissance utilisés pour distinguer de nombreuses odeurs. Plusieurs travaux ont été publiés sur l’utilisation du nez électronique dans des applications spécifiques. Cependant, il n’y a pas un grand nombre des travaux sur les nez artificiels qui peuvent être utilisés dans plusieurs applications. Ce projet a comme objectif la conception et la fabrication d’un nez électronique qui peut être utilisé dans plusieurs applications selon les besoins d’utilisateur. Une conception et une fabrication de la partie matérielle ont été faites à partir de zéro. Elle contient le système d’échantillonnage qui facilite la réaction des gaz avec les capteurs et la carte électronique qui traduit ces réactions en valeurs compréhensibles par la partie logicielle. Une conception, dans l’ensemble, optimale pour toutes les applications a été fabriquée à la fin de cette partie. Pour la partie logicielle, un processus d’apprentissage et de reconnaissance a été proposé en utilisant un système d’apprentissage évolutif basé sur des règles floues (FRB). L’évolution de la partie logicielle assure une flexibilité de l’ensemble (partie matérielle et partie logicielle) aux besoins d’utilisateurs. Afin de diminuer la dépendance du système à l’égard d’utilisateurs, une méthode de supervision active a été utilisée avec le système d’apprentissage et de reconnaissance

Improved results on an extended dissipative analysis of neural networks with additive time-varying delays using auxiliary function-based integral inequalities

The issue of extended dissipative analysis for neural networks (NNs) with additive time-varying delays (ATVDs) is examined in this research. Some less conservative sufficient conditions are obtained to ensure the NNs are asymptotically stable and extended dissipative by building the agumented Lyapunov-Krasovskii functional, which is achieved by utilizing some mathematical techniques with improved integral inequalities like auxiliary function-based integral inequalities (gives a tighter upper bound). The present study aims to solve the $H_{\infty}, L_2-L_{\infty}$, passivity and $(Q, S, R)$-$\gamma$-dissipativity performance in a unified framework based on the extended dissipativity concept. Following this, the condition for the solvability of the designed NNs with ATVDs is presented in the form of linear matrix inequalities. Finally, the practicality and effectiveness of this approach were demonstrated through four numerical examples

Generalized Logistic Models and its orthant tail dependence

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009)