Abstract. We set general conditions under which the general poverty index, which summarizes all the available indices, is asymptotically represented with some empirical processes. This representation theorem offers a general key, in most directions, for the asymptotic of the bulk of poverty indices and issues in poverty analysis. Our representation results uniformly hold on a large collection of poverty indices. They enable the continuous measure of poverty with longitudinal data.Résumé. Nous introduisons un ensemble cohérent de conditions sous lesquelles, l'Index Général de Pauvreté, qui englobe presque tous les indices usuels, admet une représentation asymptptique sous forme de somme d'un processus empirique fonctionnel et d'un processus empirique spécial. Cette représentation asymptotique offre un ensemble d'outils permettant de trouver rapidement les lois asymptotiques des mesures de pauvreté. Elle est en général utile pour l'analyse de la pauvreté. Elle est donnée de manière uniforme par rapport au temps età la fonctionnelle de la mesure. Elle est appropriée pour l'étude de la pauvreté longitudinale.

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In this paper, we show that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are gathered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or Lower Threshold Based (LTH). These statistics may be time-dependent when the scene is monitored in the time and depend on specific functions w and d. This paper provides time-dependent and uniformly functional weak asymptotic laws that allow temporal and spatial studies of the risk as well as comparison among statistics in terms of dependence and mutual influence. The results are particularized for usual statistics like the Kakwani and Shorrocks ones that are mainly used in welfare analysis. Data-driven applications based on pseudo-panel data are provided.