Formulas
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(→Probability Density Functions (PDFs)) |
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* [http://en.wikipedia.org/wiki/Exponential_distribution Exponential] PDF: <math> | * [http://en.wikipedia.org/wiki/Exponential_distribution Exponential] PDF: <math> | ||
\lambda e^{-\lambda x},\; x \ge 0</math> | \lambda e^{-\lambda x},\; x \ge 0</math> | ||
- | * [http://socr.ucla.edu/htmls/dist/Fisher_Distribution.html F Distribution] PDF: <math> \frac {(\frac {d_1 x}{d_1 x + d_2})^{ d_1/2} ( 1 - \frac {d_1 x} {d_1 x + d2}) ^ {d_2/2}} { xB(d_1/2 , d_2/2) } | + | * [http://socr.ucla.edu/htmls/dist/Fisher_Distribution.html F Distribution] PDF: <math> \frac {(\frac {d_1 x}{d_1 x + d_2})^{ d_1/2} ( 1 - \frac {d_1 x} {d_1 x + d2}) ^ {d_2/2}} { xB(d_1/2 , d_2/2) } </math> |
==Transformations== | ==Transformations== |
Revision as of 06:02, 21 October 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:
- F Distribution 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).
- Gamma to Beta Transformation: .
- Student's T to Standard Normal Transformation:
- Student's T to Cauchy Transformation:
- Cauchy to General Cauchy Transformation:
- General Cauchy to Cauchy Transformation:
- SOCR Home page: http://www.socr.ucla.edu
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