Applications of Marshall–Olkin Fréchet Distribution

In this article, we consider the applications of Marshall–Olkin Fréchet distribution. The reliability of a system when both stress and strength follows the new distribution is discussed and related characteristics are computed for simulated data. The model is applied to a real data set on failure times of air-conditioning systems in jet planes and reliability is estimated. We also develop acceptance sampling plan for the acceptance of a lot whose lifetime follows this distribution. Four different autoregressive time series models of order 1 are developed with minification structure as well as max-min structure having these stationary marginal distributions. Some properties of the models are also established.     

The Family and Work in the Post-socialist Transition of Serbia: 1991–2006

For a long period of time, the family and the household have not been considered agents in the economic sphere. However, in contemporary theoretical and research practice we are witnessing a rehabilitation of this aspect of family activity. The importance of the broader social and economic impact of this activity of families and households is legitimated through the concepts of social capital and household strategies in the labor sphere. This paper presents the results of three successive representative empirical studies of households in Serbia between 1991 and 2006. The main goal of these studies was to observe the problems households and families are facing in the transition process. The specific profile of Serbia's transition path, determined by numerous societal disturbances, is emphasized. The relation between the work sphere and the family sphere is viewed through five forms of the working status and activities of household members. Research results show a remarkable proliferation of informal work activities, which enable the survival of households in the circumstances of high unemployment and low wages in the formal labor sector.     

Towards the strategies of modern societies: systems and social processes

While several sociological theories have traditionally dealt with rational action by human actors, little attention has been devoted to the possibilities for rational steering of the entire subsystems of functionally differentiated modern societies in the context of their increasing complexity. Although rational intentional action is clearly limited at the macro-level by the complexity emphasized by Luhmann's social systems theory, strategies are required to approach the normative ideal of active society as defined by Etzioni. Understanding the strategic processes requires micro–macro and agency–structure connections. A possible solution to understanding strategy as a social process in this respect is found in the adaptation of the three-level – individuality, reality and totality – approach of Sztompka's theory of social becoming.     

Complement to a comparative analysis of heuristics for the <Emphasis Type="Italic">p</Emphasis>-median problem

A recent comparison of evolutionary, neural network, and scatter search heuristics for solving the p-median problem is completed by (i) gathering or obtaining exact optimal values in order to evaluate errors precisely, and (ii) including results obtained with several variants of a variable neighborhood search (VNS) heuristic. For a first, well-known, series of instances, the average errors of the evolutionary and neural network heuristics are over 10% and more than 1000 times larger than that of VNS. For a second series, this error is about 3% while the errors of the parallel VNS and of a hybrid heuristic are about 0.01% and that of parallel scatter search even smaller.     

A new family of lifetime models

We introduce a new family of distributions by adding a parameter to the Marshall–Olkin family of distributions. Some properties of the new family of distributions are derived. A particular case of the family, a three-parameter generalization of the exponential distribution, is given special attention. The shape properties, moments, distributions of the order statistics, entropies and estimation procedures are derived. An application to a real data set is discussed.     

On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization

This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is “matched” to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.     

Confidence intervals for the ratio of two variances

In this paper we consider confidence intervals for the ratio of two population variances. We propose a confidence interval for the ratio of two variances based on the t-statistic by deriving its Edgeworth expansion and considering Hall's and Johnson's transformations. Then, we consider the coverage accuracy of suggested intervals and intervals based on the F-statistic for some distributions.