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

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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.
Keywords
lower distribution function, coherent lower prevision, lower Riemann–Stieltjes integral, complete monotonicity, moment sequence

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Citation

Please use this url to cite or link to this publication:

Chicago
Miranda, Enrique, Gert De Cooman, and Erik Quaeghebeur. 2008. “Finitely Additive Extensions of Distribution Functions and Moment Sequences: The Coherent Lower Prevision Approach.” International Journal of Approximate Reasoning 48 (1): 132–155.
APA
Miranda, E., De Cooman, G., & Quaeghebeur, E. (2008). Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach. International Journal of Approximate Reasoning, 48(1), 132–155.
Vancouver
1.
Miranda E, De Cooman G, Quaeghebeur E. Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach. International Journal of Approximate Reasoning. Elsevier; 2008;48(1):132–55.
MLA
Miranda, Enrique, Gert De Cooman, and Erik Quaeghebeur. “Finitely Additive Extensions of Distribution Functions and Moment Sequences: The Coherent Lower Prevision Approach.” International Journal of Approximate Reasoning 48.1 (2008): 132–155. Print.
@article{397873,
  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.},
  author       = {Miranda, Enrique and De Cooman, Gert and Quaeghebeur, Erik},
  issn         = {0888-613X},
  journal      = {International Journal of Approximate Reasoning},
  keyword      = {lower distribution function,coherent lower prevision,lower Riemann--Stieltjes integral,complete monotonicity,moment sequence},
  language     = {eng},
  number       = {1},
  pages        = {132--155},
  publisher    = {Elsevier},
  title        = {Finitely additive extensions of distribution functions and moment sequences: The coherent lower prevision approach},
  url          = {http://dx.doi.org/10.1016/j.ijar.2007.07.007},
  volume       = {48},
  year         = {2008},
}

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