The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

On the structure of cooperative and competitive solutions for a generalized assignment game

We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two al- ternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of ma- trices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.

Enseñar a convivir, enseñar a comunicarse = Teaching to live together, teaching to communicate

In this article we look at some of the questions related to the learning of how to live together so that we may then look more closely at the relative aspects of the learning of language. We insist on the importance of the not strictly linguistic aspects associated to the incorporation of children from immigrant families to the schools. From this point of view we underline the heterogeneous nature of the situation in which these children find themselves (in function with the social and professional situation of the family, of having been born here or not, and of having or not previous school experience in the community of origin etc). We also look at the necessary eradication of stereo types in the treating of this problem. We then discuss some strategies where there can be joint collaboration in the school for attaining these objectives