# Formulas

(Difference between revisions)
 Revision as of 19:20, 24 April 2008 (view source)IvoDinov (Talk | contribs) (typo)← Older edit Revision as of 19:24, 24 April 2008 (view source)IvoDinov (Talk | contribs) (added Student's T PDF)Newer edit → Line 6: Line 6: * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma] PDF: $x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!$ * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma] PDF: $x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!$ * [http://en.wikipedia.org/wiki/Beta_distribution Beta] PDF: $\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1}\!$ * [http://en.wikipedia.org/wiki/Beta_distribution Beta] PDF: $\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1}\!$ + * [http://en.wikipedia.org/wiki/Student's_t_distribution Student's T] PDF: $\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}\!$

## Revision as of 19:24, 24 April 2008

This SOCR Wiki page contains a number of formulas, mathematical expressions and symbolic representations that are used in varieties of SOCR resources. Usage is defined as a reference by image, text, TeX, URL, etc. For instance the SOCR Distributome project uses these formulas to represent PDFs, CDFs, transformations, etc.

• Standard Normal PDF: $f(x)= {e^{-x^2} \over \sqrt{2 \pi}}$
• General Normal PDF: $f(x)= {e^{{-(x-\mu)^2} \over 2\sigma^2} \over \sqrt{2 \pi\sigma^2}}$
• Chi-Square PDF: $\frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}\,$
• Gamma PDF: $x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!$
• Beta PDF: $\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\, x^{\alpha-1}(1-x)^{\beta-1}\!$
• Student's T PDF: $\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{x^2}{\nu} \right)^{-(\frac{\nu+1}{2})}\!$