Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach

  • Authors:

  • Enrique Miranda;Gert de Cooman;Erik Quaeghebeur

  • Affiliations:

  • Rey Juan Carlos University, Department of Statistics and Operations Research. C-Tulipán, s/n 28933 Móstoles, Spain;Ghent University, SYSTeMS Research Group, Technologiepark -- Zwijnaarde 914, 9052 Zwijnaarde, Belgium;Ghent University, SYSTeMS Research Group, Technologiepark -- Zwijnaarde 914, 9052 Zwijnaarde, Belgium

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

We study the information that a distribution function provides about the finitely additive probability measure inducing it. We show that in general there is an infinite number of finitely additive probabilities associated with the same distribution function. Secondly, we investigate the relationship between a distribution function and its given sequence of moments. We provide formulae for the sets of distribution functions, and finitely additive probabilities, associated with some moment sequence, and determine under which conditions the moments determine the distribution function uniquely. We show that all these problems can be addressed efficiently using the theory of coherent lower previsions.