Formulas
From Socr
(Difference between revisions)
(→Transformations) |
m (→Probability Density Functions (PDFs)) |
||
Line 15: | Line 15: | ||
\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) } </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) } </math> | ||
- | * [http://en.wikipedia.org/wiki/Bernoulli_distribution Bernoulli] | + | * [http://en.wikipedia.org/wiki/Bernoulli_distribution Bernoulli] PMF: <math> q = (1 - p) </math> for <math> k = 0, p </math> for <math> k = 1 </math> |
+ | * [http://socr.ucla.edu/htmls/dist/Binomial_Distribution.html Binomial] PMF: <math> \begin{pmatrix} n \\ k \end{pmatrix} p^k (1-p)^{n-k}</math> | ||
==Transformations== | ==Transformations== |
Revision as of 08:29, 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:
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: (iid)
- Binomial to Bernoulli: n = 1
- SOCR Home page: http://www.socr.ucla.edu
Translate this page: