Difference between revisions of "Q-Gaussian distribution"
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(Created page with "The $q$-Gaussian distribution has probability density function $$f(x)=\dfrac{\sqrt{\beta}}{C_q} e_q(-\beta x^2),$$ where $e_q$ denotes the Tsallis q-exponential|Tsallis...") |
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\dfrac{\sqrt{\pi}\Gamma( \frac{3-q}{2(q-1)} )}{\sqrt{q-1}\Gamma(\frac{1}{q-1})} &; 1<q<3. | \dfrac{\sqrt{\pi}\Gamma( \frac{3-q}{2(q-1)} )}{\sqrt{q-1}\Gamma(\frac{1}{q-1})} &; 1<q<3. | ||
\end{array} \right.$$ | \end{array} \right.$$ | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 18:55, 24 May 2016
The $q$-Gaussian distribution has probability density function $$f(x)=\dfrac{\sqrt{\beta}}{C_q} e_q(-\beta x^2),$$ where $e_q$ denotes the Tsallis $q$-exponential and $$C_q = \left\{ \begin{array}{ll} \dfrac{2\sqrt{\pi}\Gamma(\frac{1}{1-q})}{(3-q)\sqrt{1-q}\Gamma(\frac{3-q}{2(1-q)})}&; -\infty < q < 1 \\ \sqrt{\pi} &; q=1 \\ \dfrac{\sqrt{\pi}\Gamma( \frac{3-q}{2(q-1)} )}{\sqrt{q-1}\Gamma(\frac{1}{q-1})} &; 1<q<3. \end{array} \right.$$
