Kinetical foundations of non-conventional statistics

Kinetical foundations of non conventional statistics

After considering the kinetical interaction principle (KIP) introduced in ref. Physica A 296, 405 (2001), we study in the Boltzmann picture, the evolution equation and the H-theorem for non extensive systems. The q-kinetics and the κ-kinetics are studied in detail starting from the most general non linear Boltzmann equation compatible with the KIP.

On the Foundations of Statistics: a Frequentist Approach on the Foundations of Statistics: a Frequentist Approach

A limited but basic problem in the foundations of statistics is the following: Given a para-metric model, given perhaps some observations from the model, but given no prior information about the parameters (\total ignorance"), what can we say about the occurrence of a speciied event A under this model in the future (prediction problem)? Or, as probabilities are often described in terms of bets,...

On the Mathematical Foundations of Theoretical Statistics

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Some Remarks on the Foundations of Statistics

The foundations of statistics with black swans

We extend the foundation of statistics to integrate rare events that are potentially catastrophic, called black swans.These include natural hazards, regime change in complex systems, market crashes, catastrophic climate change and major episodes of species extinction. Classic statistics and physics treat such events as ‘outliers’ and often disregard them. We propose a new axiomatization of subj...