Formulas
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* [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://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> | * [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> | ||
+ | * [http://socr.ucla.edu/htmls/dist/NegativeBinomial_Distribution.html Negative Binomial] PMF: <math> \begin{pmatrix} k + r - 1 \\ k \end{pmatrix} p^r(1-p)^k </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Geometric_Distribution.html Geometric] PMF: <math> (1-p)^{k-1}p </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Erlang_Distribution.html Erlang] PDF: <math> \frac {\lambda x^{k-1}e^{-\lambda x}} {(k-1)!} </math> | ||
+ | * [http://socr.ucla.edu/htmls/dist/Laplace_Distribution.html Laplace] PDF: <math> \frac {1}{2b} \exp (- \frac{|x-\mu|}{b}) </math> | ||
==Transformations== | ==Transformations== |
Revision as of 09:53, 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: (1 − p)k − 1p
- 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: n = 1
- Binomial to General Normal Transformation:
- Binomial to Poisson Transformation:
- SOCR Home page: http://www.socr.ucla.edu
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