Some distributional properties of the generalized type 1 logistic distribution are given. Based on these distributional property a characterization of this distribution is presented

Consider a system with lifetime governed by a bivariate exponential model $\left( X,Y\right)$. Using the maximum likelihood method and the Bayesian approach, we estimate the parameters and the mean time between failure (MTBF) of this model. To compare the estimators, an exhaustive Monte Carlo study is performed using the Pitman closeness criterion and the relative efficiency.

It is proved in several works as well in finance that in economics (see, for example Timmermann 2000) that in theory the regime switching models, under stationarity hypothesis, are short memory. However, the empirical autocorrelation function (ACF) of these models decreases slowly towards zero, resembling so to that of long memory processes. In this paper we are interested to the study of the empirical behavior of the ACF of processes in order to distinguish the long memory behavior to the regime switching by using Monte Carlo simulations. Two methods are used: the one based on tests and the other on estimators of the long memory parameter. Finally, an application on real data is proposed.(Paper in French)

One of the ways of managing the risk that can arise from the changes in the relationship between assets and liabilities is by asset-liability management. Recently, Value-at-risk (VaR) and tail conditional expectation (TCE) have also emerged as standard tools for measuring and controlling the risk of trading portfolios. The limits of TCE can be transformed into the limits of VaR and conversely in some dynamical setting, TCE is preferable to VaR for being coherent. In this paper we obtain a portfolio selection model for an institution's assets- liabilities under the TCE with consumption cost and transaction cost. A set of partial differential equations are derived and closed form solution proffered, when there is no transaction cost.

We consider the problem of estimating the quadratic loss $||\delta -\theta ||^{2}$ of an estimator $\delta $ of the location parameter $\theta =(\theta _{1},\ldots ,\theta _{p})$ when a subset of the components of $\theta$ are restricted to be nonnegative. First, we assume that the random observation $X$ is a Gaussian vector and, secondly, we suppose that the random observation has the form $(X,U)$ and has a spherically symmetric distribution around a vector of the form $(\theta ,0)$ with $\dim X=\dim \theta =p$ and $\dim U=\dim 0=k$. For these two settings, we consider two location estimators, the least square estimator and a shrinkage estimators, and we compare theirs unbiased loss estimators with improved loss estimator.

We present a new exponential inequality as a generalization of that of Sung et al. Sung et al(2011) for $M$-acceptable random variables, and hence for extended negative ones. Our result is based on the simple real inequality $e^{x}\leq 1+x+(|x|/2)e^{|x|},x\in \mathbb{R}$, in place of the following one: $% e^{x}\leq 1+x+(x^{2}/2)e^{|x|},x\in \mathbb{R}$, used by many authors. We compare the given bound with former ones.

The probability distribution of a set of observation is most often defined as a convex combination of probability laws. To highlight this mixture of the laws, MCMC (Monte Carlo Markov Chain) which is an algorithm that generates a stationary Markov chain is often used; laws being considered as normal laws. In this paper, the observations are positive integer, so it is assumed that the mixture law is a Poisson weighted law and Blending laws are dual. The purpose of this work is to determine the dual laws by simple algebraic properties. (Paper in French)

The analysis of Co-inertia between two tables was generalized with the simultaneous analysis several couples of triplets of tables in STATICO in the link between two vertical multi-tables. In this article, being given the context of STATICO, we propose an analysis of successive Co-inertia (ACIs). The axes of Co-inertia which are given are common to all the tables. To interpret the variables of each table, we propose the orthogonal version of this analysis of Co-inertia which we call ACIOs. We apply this method to the real data. (Paper in French)