La médiane simpliciale d'Oja: Existence,unicité et stabilité

Oja (1983) examined various ways of measuring location, scatter, skewness, and kurtosis for multivariate distributions. Among other measures of location, he introduced a generalised median known in this paper under the name of the Oja median. In our study of the existence of that median, we show that Oja's definition can only be applied to distributions having a mean. In dimension d θ 2, we establish that the usual method of extension breaks down, which raises the question of the validity of the concept as a notion of median. Two fundamental theoretical properties of that median are also considered: uniqueness and consistency.     

Measuring credibility of compensatory preference statements when trade-offs are interval determined

This paper studies how an overall fuzzy preference relation can be constructed in the compensatory context of the simple additive difference model, when imprecision on the trade-offs has to be taken into account. Three credibility indices of preferences are analysed and illustrated by a numerical example. Arguments are presented supporting the use of the third index, for which an interesting transitivity property (which was an open problem) is proved.     

Human Capital,Trade Openness and Growth in Argentina in the 20th Century

We estimate a production function that accounts for the economic performance of the country in the 20th century. We elaborate long term time series whereas most of the recent empirical studies on growth are based on cross section analysis. This approach allows us to follow the various regime changes that can be identified in the rich economic history of Argentina. To evaluate Total Factor Productivity (TFP) we initially test the classical Solow Model. We estimate the speed of convergence of TFP and obtain a non convergence result. This speed of convergence has declined since the 1930s, and we find a phenomenon of divergence in the period 1970–90. We then analyse the impact on production of additional variables recently highlighted in the endogenous growth literature such as the process of catch up of foreign technical progress, human capital and trade openness. Chow tests for this extended production function give us a strong probability of changes in the growth regimes. The estimation, that takes into consideration the break points identified, shows that the impact of trade openness and foreign technology is not stable throughout the century. In what concerns the impact of education on economic growth, we find a strong effect of primary education on growth, and a weaker effect of secondary-university education.     

A class of bivariate regression models for discrete and/or continuous responses

ABSTRACT

A general class of models for discrete and/or continuous responses is proposed in which joint distributions are constructed via the conditional approach. It is assumed that the distributions of one response and of the other response given the first one belong to exponential family of distributions. Furthermore, the marginal means are related to the covariates by link functions and a dependency structure between the responses is inserted into the model. Estimation methods, diagnostic analysis and a simulation study considering a Bernoulli-exponential model, a particular case of the class, are presented. Finally, this model is used in a real data set.     

Waiting time to exhaust lottery numbers

Questions related to lotteries are usually of interest to the public since people think there is a magic formula which will help them to win lottery draws. This note shows how to compute the expected waiting time to observe specific numbers in a sequence of lottery draws and show that surprising facts are expected to occur.     

Accuracy of approximate progressively censored reliability sampling plans for exponential models

Reliability sampling plans provide an efficient method to determine the acceptability of a product based upon the lifelengths of some test units. Usually, they depend on the producer and consumer’s quality requirements and do not admit closed form solutions. Acceptance sampling plans for one- and two-parameter exponential lifetime models, derived by approximating the operating characteristic curve, are presented in this paper. The accuracy of these approximate plans, which are explicitly expressible and valid for failure and progressive censoring, is assessed. The approximation proposed in the one-parameter case is found to be practically exact. Explicit lower and upper bounds on the smallest sample size are given in the two-parameter case. Some additional advantages are also pointed out.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.     

Exploring the characteristics of rotating electric machines with factor analysis

Applications of multivariate statistics in engineering are hard to find, apart from those in quality control. However, we think that further insight into some technological cases may be gained by using adequate multivariate analysis tools. In this paper, we propose a review of the key parameters of rotating electric machines with factor analysis. This statistical technique allows not only the reduction of the dimension of the case we are analysing, but also reveals subtle relationships between the variables under study. We show an application of this methodology by studying the interrelations between the key variables in an electric machine, in this case the squirrel-cage induction motor. Through a step-by-step presentation of the case study, we deal with some of the topics an applied researcher may face, such as the rotation of the original factors, the extraction of higher-order factors and the development of the exploratory model. As a result, we present a worthwhile framework to both confirm our previous knowledge and capture unexplored facts. Moreover, it may provide a new approach to describing and understanding the design, performance and operating characteristics of these machines.     

A Multivariate Indicator to Compute Middle Class Population

Social Indicators Research - Monitoring progress towards the Sustainable Development Goals by 2030 requires the global community to disaggregate targets along socio-economic lines, but little has...