Functional Weak Laws for the Weighted Mean Losses or Gains and Applications

Pape Djiby  Mergane; Gane Samb  Lo; Serigne Touba  Sall

doi:10.4236/am.2015.65079

Gane Samb Lo^1,2, Serigne Touba Sall^1,3, Pape Djiby Mergane¹

Abstract: 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.

Keywords: Empirical Process, Time Dependent Process, Weak Theory, Risk Measures, Poverty Index, Loss Function, Economic Welfare

Cite this paper: Lo, G. , Sall, S. and Mergane, P. (2015) Functional Weak Laws for the Weighted Mean Losses or Gains and Applications. Applied Mathematics, 6, 847-863. doi: 10.4236/am.2015.65079.

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