On φ-Families of Probability Distributions |
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Authors: | Rui F Vigelis Charles C Cavalcante |
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Institution: | 1. Computer Engineering, Campus Sobral, Federal University of Ceará, Fortaleza, CE, Brazil 2. Wireless Telecommunication Research Group, Department of Teleinformatics Engineering, Federal University of Ceará, Fortaleza, CE, Brazil
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Abstract: | We generalize the exponential family of probability distributions. In our approach, the exponential function is replaced by a φ-function, resulting in a φ-family of probability distributions. We show how φ-families are constructed. In a φ-family, the analogue of the cumulant-generating function is a normalizing function. We define the φ-divergence as the Bregman divergence associated to the normalizing function, providing a generalization of the Kullback–Leibler divergence. A formula for the φ-divergence where the φ-function is the Kaniadakis κ-exponential function is derived. |
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