A Probability Distribution Of Functional Random Variable With A Functional Data Analysis Application

Probability distributions are central tools for probabilistic modeling in data mining, and they lack in functional data analysis (FDA). In this paper we propose a probability distribution law for functional data. We build it using jointly the quasi-arithmetic means and the generators of Archimedean copulas. We also define a density adapted to the infinite dimension of the space of functional data. For this we use the Gateaux differential. We illustrate the utility of this tool in FDA, applying it in a mixture decomposition classification