Formulas
From Socr
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* [http://en.wikipedia.org/wiki/Normal_distribution Standard Normal to Chi-Square Transformation]: <math>\sum_{k=1}^{\nu} X_k^2</math> | * [http://en.wikipedia.org/wiki/Normal_distribution Standard Normal to Chi-Square Transformation]: <math>\sum_{k=1}^{\nu} X_k^2</math> | ||
* [http://en.wikipedia.org/wiki/Gamma_distribution Gamma to General Normal Transformation]: <math>\mu=\alpha\times\beta;\sigma^2=\alpha^2\times\beta;\beta\longrightarrow\infty</math> | * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma to General Normal Transformation]: <math>\mu=\alpha\times\beta;\sigma^2=\alpha^2\times\beta;\beta\longrightarrow\infty</math> | ||
- | * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma to | + | * [http://en.wikipedia.org/wiki/Gamma_distribution Gamma to Exponential Transformation]: The special case of <math>{\Gamma}(k=1, \theta=1/\lambda)\,</math> is equivalent to exponential <math>Exp(\lambda)</math>. |
Revision as of 20:39, 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.
Probability Density Functions (PDFs)
- Standard Normal PDF:
- General Normal PDF:
- Chi-Square PDF:
- Gamma PDF:
- Beta PDF:
- Student's T PDF:
- Poisson PDF:
- Chi PDF:
- Cauchy PDF:
- Exponential PDF:
Transformations
- Standard Normal to General Normal Transformation:
- General Normal to Standard Normal Transformation:
- Standard Normal to Chi Transformation:
- Standard Normal to Chi-Square Transformation:
- Gamma to General Normal Transformation:
- Gamma to Exponential Transformation: The special case of is equivalent to exponential Exp(λ).
- SOCR Home page: http://www.socr.ucla.edu
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