Formulas
From Socr
(Difference between revisions)
m (→Transformations) |
m (→Transformations) |
||
Line 44: | Line 44: | ||
* [http://socr.ucla.edu/htmls/dist/Erlang_Distribution.html Erlang to Chi-Square Transformation]: <math> \begin{pmatrix} \alpha = 2 \end{pmatrix} </math> | * [http://socr.ucla.edu/htmls/dist/Erlang_Distribution.html Erlang to Chi-Square Transformation]: <math> \begin{pmatrix} \alpha = 2 \end{pmatrix} </math> | ||
* [http://socr.ucla.edu/htmls/dist/Laplace_Distribution.html Laplace to Exponential Transformation]: <math>\begin{pmatrix} \begin{vmatrix} X \end{vmatrix} \\ \alpha_1 = \alpha_2 \end{pmatrix}</math> | * [http://socr.ucla.edu/htmls/dist/Laplace_Distribution.html Laplace to Exponential Transformation]: <math>\begin{pmatrix} \begin{vmatrix} X \end{vmatrix} \\ \alpha_1 = \alpha_2 \end{pmatrix}</math> | ||
- | * [http://socr.ucla.edu/htmls/dist/Laplace_Distribution.html Laplace to Exponential Transformation]: <math> x_1 - x_2 \</math> | + | * [http://socr.ucla.edu/htmls/dist/Laplace_Distribution.html Laplace to Exponential Transformation]: <math> x_1 - x_2 \ </math> |
Revision as of 10:56, 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:
- Bernoulli PMF: q = (1 − p) for k = 0,p for k = 1
- Binomial PMF:
- Negative Binomial PMF:
- Geometric PMF:
- Erlang PDF:
- Laplace 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:
- Fisher's F to Student's T:
- Student's T to Fisher's F: X2
- Bernoulli to Binomial Transformation: (iid)
- Binomial to Bernoulli Transformation:
- Binomial to General Normal Transformation:
- Binomial to Poisson Transformation:
- Negative Binomial to Geometric Transformation:
- Erlang to Exponential Transformation:
- Erlang to Chi-Square Transformation:
- Laplace to Exponential Transformation:
- Laplace to Exponential Transformation:
- SOCR Home page: http://www.socr.ucla.edu
Translate this page: