Difference between revisions of "Formulas"
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* [http://en.wikipedia.org/wiki/Chi-square_distribution Chi-Square] PDF: <math>\frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}\,</math> | * [http://en.wikipedia.org/wiki/Chi-square_distribution Chi-Square] PDF: <math>\frac{(1/2)^{k/2}}{\Gamma(k/2)} x^{k/2 - 1} e^{-x/2}\,</math> | ||
* [http://en.wikipedia.org/wiki/Gamma_distribution Gamma] PDF: <math>x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!</math> | * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma] PDF: <math>x^{k-1} \frac{\exp{\left(-x/\theta\right)}}{\Gamma(k)\,\theta^k}\,\!</math> | ||
| + | * [http://en.wikipedia.org/wiki/Beta_distribution Beta] PDF: <math>\frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}\!</math> | ||
Revision as of 14:25, 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\[\frac{x^{\alpha-1}(1-x)^{\beta-1}} {\mathrm{B}(\alpha,\beta)}\!\]
