Cardinal likelihoods: A joint characterization of the logarithmic and linear likelihood functions

Mitsunobu Miyake

No 402, TERG Discussion Papers from Graduate School of Economics and Management, Tohoku University

Abstract: A likelihood function is a real-valued function on the set of events of the sample space representing the likelihood of the occurrence of the events, and the logarithmic and linear (positive affine) likelihood functions are given by the logarithmic and linear transformations of a probability measure on the events, respectively. Specifying statistician's subjective likelihood of the events by a difference comparison relation, this paper provides some axioms for the relations to be represented cardinally by the two likelihood functions, the probability measures of which coincide with the unique subjective (conditional) probability measure determined by the relation. This result turns out that the difference of the axiomatizations for the likelihood functions is only the difference of the Lucian independence axioms, (i.e., difference in the definition of irrelevant events for the relations).

Pages: 28 pages
Date: 2019-03
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10097/00126154

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:toh:tergaa:402

Access Statistics for this paper

More papers in TERG Discussion Papers from Graduate School of Economics and Management, Tohoku University Contact information at EDIRC.
Bibliographic data for series maintained by Tohoku University Library ().