Imprecise probability through f-probability and its statistical physical implications. (October 2020) - Chung, Won Sang; Algin, Abdullah
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