Imprecise probability through f-probability and its statistical physical implications

Won Sang Chung and Abdullah Algin

Chaos, Solitons & Fractals, 2020, vol. 139, issue C

Abstract: In this work, we present an approach to describe imprecise probability through an effective probability theory, called the f-probability. We develop a bijective and monotonous map from the precise probability in order to construct the f-probability theory based on the f-addition, f-subtraction, f-multiplication and f-division. We apply the f-probability to the Bernoulli trial and derive the f-binomial distribution. Finally, we obtain the non-extensive entropy through the f-probability theory, and give its statistical physical implications on several areas of potential applications. PACS number(s): 02.50.Cw, 05.20.-y; 05.90.+m

Keywords: Foundations of probability; Imprecise probabilities; Uncertainty measures; Non-extensivity; Deformed calculus; Complex systems; Non-linear dynamics (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304185

DOI: 10.1016/j.chaos.2020.110020

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