Le lambda-inferenze induttive: caratterizzazione e proprietà

Abstract

We analyze the properties of those methods of statistical inferences which arrive at an evaluation of the predictive probability .... (1) for which the (s + 1)-th observation has a given modality j given the d-tuple s of absolute frequencies of s observations of a variable having d qualitative modalities. 
We consider those hypotheses from which it is possible to deduce the (1) in the case ß> 0, and we determine each of those implications which exist among them. Then we extend the study to the case (- inf < ß < + inf), suggested by more recent works, and we study its properties. In this way we obtain a set of inferences which include many known inferences, such as: the direct rule, the succession rule of Laplace, the statistics of Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac.