Estimators, escort probabilities, and phi-exponential families in statistical physics

Abstract

The lower bound of Cramer and Rao is generalized to pairs of families of probability distributions, one of which is escort to the other. This bound is optimal for certain families, called phi-exponential in the paper. Their dual structure is explored.

19 pages, LATEX

References in corpus (4)

• Geometry of escort distributions
• Generalized thermostatistics based on deformed exponential and logarithmic functions
• Generalized thermostatistics and mean-field theory
• Continuity of a class of entropies and relative entropies

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