- There may be confusion here. Certainly, the present inline citation numbered 6 (Dragulescu) uses the name "Tsallis distribution" for a different density function than that set out here. Whereas the one other reference I can access does use "Tsallis distribution" for the density given here. Possibly we need to be thinking of "Tsallis distributions" as a class of distributions derived from the [[Tsallis entropy}}, each one with a different constraint in deriving a maximum entropy distribution, with the "q-Gaussian" being one of the specific forms. But is this right? Melcombe (talk) 09:13, 24 June 2011 (UTC)
You are correct. Using the standard maximum entropy procedure gives the Normal distribution, and if we constrain our domain to be positive we get the exponential distribution. The Tsallis analogs are the q-gaussian and the q-exponential distributions, both of which have been called the "Tsallis Distribution". I suppose there are two approaches of which I favor the first:
1) Create a q-gaussian page and q-exponential pdf page for the distributions in addition to a Tsallis Distribution page that describes the procedure and quickly links to the two distributions or
2) Fit both distributions on the Tsallis Distribution page. Purple Post-its (talk) 15:09, 24 June 2011 (UTC)
- The page Tsallis statistics should have its (limited) content merged with a discussion of the derivation, interpretation, application and critisicm of Tsallis' work. Material can also be leveraged from Tsallis entropy, Constantino Tsallis, and Nonextensive entropy to create the central page. Then two pdf pages can be created just to describe the characteristics and applications of the respective pdfs. The outstanding question would be whether to call this central page Tsallis Statistics, Tsallis Distribution, or something different altogether. It's not necessary to name it first however, and I can start on this task prior to finalizing naming conventions. Purple Post-its 17:04, 24 June 2011 (UTC) — Preceding unsigned comment added by Purple Post-its (talk • contribs)
- Scratch that. New plan described below.Purple Post-its (talk) 13:33, 27 June 2011 (UTC)
Over the next couple weeks I plan on continuing to work on the various Tsallis pages and I figured I'd sketch out the plan. Note that this comment is linked to from 6 Tsallis related pages.
- a) Tsallis statistics should describe the mathematical operations that accompany Tsallis' work. For example, have subsections for the q-exponential, q-logarithm, escort probability, etc. These will be linked to from the other pages.
- b) Tsallis Entropy seems good, but should discuss the Tsallis Distributions and have applications. Possibly merge in Nonextensive entropy?
- c) Tsallis distribution can describe the modified Max Entropy procedure for generating distributions from Tsallis Entropy
- d) q-Gaussian and q-exponential distribution are two Probability Densitys. They need graphs, basic characterizations, special cases, methods for generating random deviates, etc.
- e) Constantino Tsallis' page needs to be cleaned up a little bit (links and references especially). Some of the material shoud likely be moved/copied to Tsallis Statistics or Tsallis Entropy page too.
- f) I'd also like to integrate this into the Template:Statistical mechanics topics and possibly other pages as well.
- g) It seems that a critiscm/critique section should be placed in one of these pages, not necessarily requiring its own page. The intro to Tsallis Entropy has a start on this. Thoughts?
- h) Is it worthwhile to create a Navigation Template of some type for navigating through these pages?
- i) There should also be thorough linking between these 6 pages. Purple Post-its (talk) 14:06, 27 June 2011 (UTC)
- Done with many of the items listed above. Still need to add/finish the following
- 1) Tsallis distribution should describe the modified Max Entropy procedure for generating distributions from Tsallis Entropy
- 2) Constantino Tsallis' page needs to be cleaned up a little bit (links and references especially). Some of the material shoud likely be moved/copied to Tsallis Statistics or Tsallis Entropy page too.
- 3) critiscm/critique section should be added somewhere
- 4) an article (or section) on the q-central limit theorem would be helpful
- 5) More text needed in general linking the concepts and probability distributions to the science behind it
- Purple Post-its (talk) 17:13, 5 July 2011 (UTC)