V. A. González-López

A new index to measure positive dependence in trivariate distributions

We introduce a new index to detect dependence in trivariate distributions. The index is based on the maximization of the coefficients of directional dependence over the set of directions. We show how to calculate the index using the three pairwise Spearmans rho coefficients and the three common 3-dimensional versions of Spearmans rho. We obtain the asymptotic distributions of the empirical processes related to the estimators of the coefficients of directional dependence and also we derive the asymptotic distribution of our index. We display examples where the index identifies dependence undetected by the aforementioned 3-dimensional versions of Spearmans rho. The value of the new index and the direction in which the maximal dependence occurs are easily computed and we illustrate with a simulation study and a real data set.

A copula model to analyze minimum admission scores

The Asymmetric Cubic Sections copula family is used to describe the dependence between language and mathematics scores of admission test. The parameters of the copula are annually estimated by means of a non-informative Bayesian method. The application focus on measuring the impact of conditioning language result to a mathematics minimum grade and vice-versa, this paper shows some initial results in that line. In addition, the analytical expression for each conditional expectation is shown together with a description of its monotonic behavior.

Modeling of Acoustic Signal Energies with a Generalized Frank Copula. A Linguistic Conjecture is Reviewed

In this article a generalized Frank copula was selected to model the dependence between the energy on two frequency bands of the speech signal, coming from eight languages. An algorithm was developed that uses maximum likelihood to choose the best fitting copula’s parameters. Through bootstrap, the algorithm estimates the variability of the parameters for each language and also computes confidence regions by means of Voronoi tesselations. A linguistic conjecture which claims that the languages are organized in three rhythmic classes, was confirmed by the Voronoi regions. Modeling with a uniparametric Frank copula, the different degrees of dependence between the energies were quantified.

Robust model selection and the statistical classification of languages

In this paper we address the problem of model selection for the set of finite memory stochastic processes with finite alphabet, when the data is contaminated. We consider m independent samples, with more than half of them being realizations of the same stochastic process with law Q, which is the one we want to retrieve. We devise a model selection procedure such that for a sample size large enough, the selected process is the one with law Q. Our model selection strategy is based on estimating relative entropies to select a subset of samples that are realizations of the same law. Although the procedure is valid for any family of finite order Markov models, we will focus on the family of variable length Markov chain models, which include the fixed order Markov chain model family. We define the asymptotic breakdown point (ABDP) for a model selection procedure, and we show the ABDP for our procedure. This means that if the proportion of contaminated samples is smaller than the ABDP, then, as the sample size g...

Consistent Estimation of Partition Markov Models

The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.

Full Bayesian Analysis for a Model of Tail Dependence

The family of the asymmetric logistic copulas appears naturally in modeling tail dependence. Within this family, some well-known models, as independence and logistic dependence, define precise hypotheses, having zero posterior probability for an absolute continuous posterior distribution. We show that the e-value associated to the Full Bayesian Significance Test has a good performance in non standard dependence problems, obtaining posterior estimates and predictive distributions. The analysis proposed is illustrated with two examples: (1) monthly sea level maxima at Newlyn and Sheerness, England (1990–2005) and (2) AIDS rates related to an educational indicator in U.S. Census Bureau (2007). We validate the inferences obtained through simulated data.

A copula-based partition Markov procedure

ABSTRACT The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain, and when the size of the database is not large enough, it is not possibly a consistent estimation. In this paper, we introduce a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consists in obtaining a partition of the state space which is constructed from a combination of the partitions corresponding to the marginal processes and the partitions corresponding to the multivariate Markov chain.

E-Bayesian estimation for system reliability and availability analysis based on exponential distribution

ABSTRACT The main purpose of this article is to introduce the E-Bayesian approach to gain flexibility in the reliability-availability system estimation. This approach will be used in series systems, parallel systems, and k-out-of-m systems, based on exponential distribution under squared error loss function, when time is continuous. We use three prior distributions to investigate its impact on the E-Bayesian approach, those prior distributions cover a big spectrum of possibilities. We show in real examples and also by simulations, how the procedure behaves. In the simulation study also we explore the impact on this estimation approach, when the number of components of the system increases.

Optimization of Queuing Theory Based on Vague Environment

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

Bounds for the cumulative conditional expectation function

We introduce the concept of cumulative conditional expectation function. This is a quantity that provides statistical support for making decisions in applied problems. The goal of this paper is to find an analytical expression for upper and lower bounds of this function, assuming stochastic dependence types as being the underlying random structure.