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Estimators, Escort Probabilities, and $\phi$-Exponential Families in Statistical Physics  
 
  Authors: Jan Naudts,  
  Keywords: Escort probability, Lower bound of Cramer and Rao, Generalized exponential family, Statistical manifold, Nonextensive thermostatistics.  
  Date Received: 23/02/04  
  Date Accepted: 11/11/04  
  Subject Codes:

82B30, 62H12

  
  Editors: Charles E. M. Pearce,  
 
  Abstract:

The lower bound of Cram�r 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. They satisfy a variational principle with respect to an appropriately chosen entropy functional, which is the dual of a free energy functional.;


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