Imprecise probability through f-probability and its statistical physical implications. (October 2020)

• Record Type: Journal Article
• Authors: Chung, Won Sang; Algin, Abdullah
• Is Part Of: Chaos, solitons and fractals. Volume 139(2020)
• Publication Date: 2020-10
• Subjects: Foundations of probability -- Imprecise probabilities -- Uncertainty measures -- Non-extensivity -- Deformed calculus -- Complex systems -- Non-linear dynamics; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110020
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: An effective probability theory called the f -probability is proposed. The properties of f -calculus are presented. The f -binomial distribution is constructed. -A new form for the non-extensive entropy called the f -entropy is devised. Imprecise probability can be modeled by the f -probability theory. 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