Alternative definitions of bivariate equilibrium distributions

The concept of equilibrium distribution plays an important role in survival analysis, reliability and insurance studies. If we consider the problem of extending this concept to higher dimensions, we do not have a unique solution. In this paper, alternative definitions of bivariate equilibrium distributions are studied and proposed. The Navarro et al. (2006) proposal is considered and some new results are given. We continue with the Gupta and Sankaran's (1998) definition. Necessary and sufficient conditions for its existence are stated and a characterization theorem is given. As a third alternative, a new definition based on conditional specification is introduced and several results are obtained. Reliability properties of the different versions are studied.     

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specified models and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order.     

Power indices expressed in terms of minimal winning coalitions

A voting situation is given by a set of voters and the rules of legislation that determine minimal requirements for a group of voters to pass a motion. A priori measures of voting power, such as the Shapley–Shubik index and the Banzhaf value, show the influence of the individual players in a voting situation and are calculated by looking at marginal contributions in a simple game consisting of winning and losing coalitions derived from the legislative rules. We introduce a new way to calculate these measures directly from the set of minimal winning coalitions and derive explicit formulae for the Shapley–Shubik and Banzhaf values. This new approach logically appealing as it writes measures as functions of the rules of the legislation. For certain classes of games that arise naturally in applications the logical shortcut drastically simplifies the numerical calculations to obtain the indices. The technique generalises directly to all semivalues.     

La Identidad y Caracter Nacionales en Mexico—La Frontera de Tamaulipas—

Resumen

En este artículo se analizan los datos de cuatro ciudades fronterizas de México. Estas son evaluaciones sobre el carácter e identidad nacional, inferidas a partir del sentido de pertenencia y participación de los ciudadanos en las instituciones más importantes de su Estado. Los resultados muestran que los habitantes de las ciudades fronterizas tienen un sentimiento de pertenencia muy reducido y un aún menor sentimiento de participación en las instituciones.     

Demographic and Motivation Differences Among Online Sex Offenders by Type of Offense: An Exploration of Routine Activities Theories

This article presents an analysis of the relationship between online sexual offenders’ demographic background and characteristics indicative of motivation and offense type. Specifically, we investigate whether these characteristics can distinguish different online sexual offender groups from one another as well as inform routine activity theorists on what potentially motivates perpetrators. Using multinomial logistic regression, this study found that online sexual offenders’ demographic backgrounds and characteristics indicative of motivation do vary by offense types. Two important implications of this study are that the term “online sexual offender” encompasses different types of offenders, including some who do not align with mainstream media’s characterization of “predators,” and that the potential offender within routine activity theory can be the focus of empirical investigation rather than taken as a given in research.     

Properties of Coherent Systems with Dependent Components

We introduce two new families of univariate distributions that we call hyperminimal and hypermaximal distributions. These families have interesting applications in the context of reliability theory in that they contain that of coherent system lifetime distributions. For these families, we obtain distributions, bounds, and moments. We also define the minimal and maximal signatures of a coherent system with exchangeable components which allow us to represent the system distribution as generalized mixtures (i.e., mixtures with possibly negative weights) of series and parallel systems. These results can also be applied to order statistics (k-out-of-n systems). Finally, we give some applications studying coherent systems with different multivariate exponential joint distributions.     

Computations of Signatures of Coherent Systems with Five Components

The signatures of coherent systems are useful tools to compute the system reliability functions, the system expected lifetimes and to compare different systems using stochastic orderings. It is well known that there exist 2, 5, and 20 different coherent systems with 2, 3, and 4 components, respectively. The signatures for these systems were given in Shaked and Suarez-Llorens (2003 Shaked , M. , Suarez-Llorens , A. ( 2003 ). On the comparison of reliability experiments based on the convolution order . Journal of the American Statistical Association 98 : 693 – 702 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). In this article, we obtain an algorithm to compute all the coherent systems with n components and their signatures. Using this algorithm we show that there exist 180 coherent systems with 5 components and we compute their signatures.     

Equilibrium Wage Dispersion with Worker and Employer Heterogeneity

We construct and estimate an equilibrium search model with on–the–job–search. Firms make take–it–or–leave–it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross–worker differences in a “competence” parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of labor. The model delivers a theory of steady–state wage dispersion driven by heterogenous worker abilities and firm productivities, as well as by matching frictions. The structural model is estimated using matched employer and employee French panel data. The exogenous distributions of worker and firm heterogeneity components are nonparametrically estimated. We use this structural estimation to provide a decomposition of cross–employee wage variance. We find that the share of the cross–sectional wage variance that is explained by person effects varies across skill groups. Specifically, this share lies close to 40% for high–skilled white collars, and quickly decreases to 0% as the observed skill level decreases. The contribution of market imperfections to wage dispersion is typically around 50%.