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.
| Original language | English |
|---|---|
| Pages (from-to) | 132-155 |
| Number of pages | 24 |
| Journal | International Journal of Approximate Reasoning |
| Volume | 48 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Apr 2008 |
| Externally published | Yes |
Funding
The authors acknowledge the support of the projects MTM2004-01269, TSI2004-06801-C04-01 and by the research grant G.0139.01 of the Flemish Fund for Scientific Research (FWO). Erik Quaeghebeur’s research is financed by a Ph.D. grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT Vlaanderen).
Keywords
- Coherent lower prevision
- Complete monotonicity
- Lower distribution function
- Lower Riemann-Stieltjes integral
- Moment sequence
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