Possibility distributions: A unified representation of usual direct probability-based parameter estimation methods

Abstract : The paper presents a possibility theory based formulation of one-parameter estimation that unifies some usual direct probability formulations. Point and confidence interval estimation are expressed in a single theoretical formulation and incorporated into estimators of a generic form: a possibility distribution. New relationships between continuous possibility distribution and probability concepts are established. The notion of specificity ordering of a possibility distribution, corresponding to fuzzy subsets inclusion, is then used for comparing the efficiency of different estimators for the case of data points coming from a symmetric probability distribution. The usefulness of the approach is illustrated on common mean and median estimators from identical independent data sample of different size and of different common symmetric continuous probability distributions.
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International Journal of Approximate Reasoning, Elsevier, 2011, 52 (9), pp.1232-1242. 〈10.1016/j.ijar.2011.04.003〉
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http://hal.univ-smb.fr/hal-00647929
Contributeur : Gilles Mauris <>
Soumis le : samedi 3 décembre 2011 - 16:19:20
Dernière modification le : mercredi 10 janvier 2018 - 09:50:07

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Gilles Mauris. Possibility distributions: A unified representation of usual direct probability-based parameter estimation methods. International Journal of Approximate Reasoning, Elsevier, 2011, 52 (9), pp.1232-1242. 〈10.1016/j.ijar.2011.04.003〉. 〈hal-00647929〉

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