First Axiom of Probability It states that the probability of any event is always a non-negative real number, i.e., either 0 or a positive real number. It cannot be negative or infinite. The smallest possible number is 0. The set of real number here includes both rational and irrational ...
S Kumar,G Ram,V Gupta - 《Journal of Applied Mathematics Statistics & Informatics》 被引量: 25发表: 2013年 Axioms for unique subjective probability on finite sets This paper discusses axioms for a comparative probability relation on a finite set which imply the existence of a unique probability...
Simple Axioms for Countably Additive Subjective Probability", UC Irvine, mimeo. Kraft, C. H., J. W. Pratt, and A. Seidenberg (1959), "Intuitive Probability on Finite Sets", Annals of Mathematical Statistics, 30: 408-419.Kopylov, I. (2010). Simple axioms for countably additive ...
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The second axiom of probability is that the probability of the entire sample space is one. Symbolically we writeP(S) = 1. Implicit in this axiom is the notion that the sample space is everything possible for our probability experiment and that there are no events outside of the sample spa...
Axioms for (α,β,γ)-entropy of a generalized probability schemeRecursive relationAdditiveSub-additiveConvex functionJensen InequalityIn this communication, we characterize a measure of information of type (α, β, γ) by taking certain axioms parallel to those considered earlier by Harvda and Char...
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For instances, para-consistency gave up the law of no contradiction, fuzzy logic relaxed the condition of excluded middle, and empiricism denied logically definable causality. Truth-based reasoning has, however, dominated philosophy and science since their beginnings. Indeed, even a probability factor ...
.TherearetwoviewsonBayesianprobabilitythatinterpretthe'stateofknowledge'conceptindifferentways.1)Objectivistview,therulesofBayesianstatisticscanbejustifiedbyrequirementsofrationalityandconsistencyandinterpretedasanextensionoflogic.2)Subjectivistview,thestateofknowledgemeasuresa'personalbelief'.SUBJECTIVEPROBABILITYSome...
These types of games are known as the games against nature in the literature. Games against nature are the games in which the payoffs in the game are unknown and the probability with which the player will choose his/her actions is entirely unknown [5,6]. Pazek and Rozman stated how a ...