Title: Cumulative distribution functions, p-boxes and decisions under risk

Authors: Ronald R. Yager

Addresses: Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA

Abstract: Our concern is with the problem of decision making in the face of incomplete or imprecise probabilistic information. We particularly focus on the use of the Cumulative Distribution Function (CDF) and the related idea of a p-box. After first describing the CDF we consider the problem of choosing between two uncertain alternatives based on their representation using CDFs. We introduce the idea of dominance as a primary rule for choosing between CDFs. Since this condition is often not satisfied, we provide a rule based on a comparison of the integrals of the CDF. We show how this is related to the expected value. The p-box, which is seen as an imprecise CDF, is introduced. We then consider the problem of choosing between alternatives whose payoffs are represented as p-boxes.

Keywords: uncertainty; decision making; imprecise probabilities; risk analysis; incomplete information; cumulative distribution function; p-boxes.

DOI: 10.1504/IJKESDP.2010.037491

International Journal of Knowledge Engineering and Soft Data Paradigms, 2010 Vol.2 No.4, pp.275 - 283

Published online: 14 Dec 2010 *

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