Tsallis distribution

<h2 id="procedure">Procedure</h2>
<p>In a similar procedure to how the <a href="/facts/Normal_distribution/UapjjPyQ">normal distribution</a> can be derived using the standard Boltzmann–Gibbs entropy or Shannon entropy, the <a href="/facts/Q-Gaussian_distribution/8X14nM96">q-Gaussian</a> can be derived from a maximization of the <a href="/facts/Tsallis_entropy/Ikjxefzh">Tsallis entropy</a> subject to the appropriate constraints.<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a><a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a>
</p>
<h2 id="common-tsallis-distributions">Common Tsallis distributions</h2>
<h3>q-Gaussian</h3>
<p>See <a href="/facts/Q-Gaussian/8X14nM96">q-Gaussian</a>.
</p>
<h3>q-exponential distribution</h3>
<p>See <a href="/facts/Q-exponential_distribution/flRkFpUM">q-exponential distribution</a>
</p>
<h3>q-Weibull distribution</h3>
<p>See <a href="/facts/Q-Weibull_distribution/uUlk652R">q-Weibull distribution</a>
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Constantino_Tsallis/IeNQpaAD">Constantino Tsallis</a></li>
<li><a href="/facts/Tsallis_statistics/97ojfQyr">Tsallis statistics</a></li>
<li><a href="/facts/Tsallis_entropy/Ikjxefzh">Tsallis entropy</a></li></ul>
<h2 id="notes">Notes</h2>

<h2 id="further-reading">Further reading</h2>
<ul><li>Juniper, J. (2007) <a href="http://www.fullemployment.net/publications/wp/2007/07-10.pdf">"The Tsallis Distribution and Generalised Entropy: Prospects for Future Research into Decision-Making under Uncertainty"</a>, Centre of Full Employment and Equity, The University of Newcastle, Australia</li>
<li>Shigeru Furuichi, Flavia-Corina Mitroi-Symeonidis, Eleutherius Symeonidis, On some properties of Tsallis hypoentropies and hypodivergences, Entropy, 16(10) (2014), 5377-5399; <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.3390%2Fe16105377">10.3390/e16105377</a></li>
<li>Shigeru Furuichi, Flavia-Corina Mitroi, Mathematical inequalities for some divergences, Physica A 391 (2012), pp. 388-400, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.physa.2011.07.052">10.1016/j.physa.2011.07.052</a>; <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://www.worldcat.org/search?fq=x0:jrnl&q=n2:0378-4371">0378-4371</a></li>
<li>Shigeru Furuichi, Nicușor Minculete, Flavia-Corina Mitroi, Some inequalities on generalized entropies, J. Inequal. Appl., 2012, 2012:226. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1186%2F1029-242X-2012-226">10.1186/1029-242X-2012-226</a></li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.cscs.umich.edu/~crshalizi/notebooks/tsallis.html">Tsallis Statistics, Statistical Mechanics for Non-extensive Systems and Long-Range Interactions</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Tsallis, C. (2009) "Nonadditive entropy and nonextensive statistical mechanics-an overview after 20 years", Braz. J. Phys, 39, 337–356 <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Box, George E. P.; Cox, D. R. (1964). "An analysis of transformations". Journal of the Royal Statistical Society, Series B. 26 (2): 211–252. JSTOR 2984418. MR 0192611. <a href="/wiki/George_E._P._Box" target="_blank">/wiki/George_E._P._Box</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Umarov, Sabir; Tsallis, Constantino; Steinberg, Stanly (2008-12-01). "On a q-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics". Milan Journal of Mathematics. 76 (1): 307–328. doi:10.1007/s00032-008-0087-y. ISSN 1424-9294. S2CID 55967725. <a href="https://doi.org/10.1007/s00032-008-0087-y" target="_blank">https://doi.org/10.1007/s00032-008-0087-y</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Prato, Domingo; Tsallis, Constantino (1999-08-01). "Nonextensive foundation of Lévy distributions". Physical Review E. 60 (2): 2398–2401. Bibcode:1999PhRvE..60.2398P. doi:10.1103/PhysRevE.60.2398. ISSN 1063-651X. PMID 11970038. <a href="https://link.aps.org/doi/10.1103/PhysRevE.60.2398" target="_blank">https://link.aps.org/doi/10.1103/PhysRevE.60.2398</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
</ol>

Tsallis distribution open-in-new

Tsallis distribution