Formulas

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*  [http://socr.ucla.edu/htmls/dist/Multinomiall_Distribution.html Multinomial] PMF: <math>f(x_1, x_2, \cdots, x_k)={n\choose x_1,x_2,\cdots, x_k}p_1^{x_1}p_2^{x_2}\cdots p_k^{x_k}</math>, where <math>x_1+x_2+\cdots+x_k=n</math>, <math>p_1+p_2+\cdots+p_k=1</math>, and <math>0 \le x_i \le n, 0 \le p_i \le 1</math>.
*  [http://socr.ucla.edu/htmls/dist/Multinomiall_Distribution.html Multinomial] PMF: <math>f(x_1, x_2, \cdots, x_k)={n\choose x_1,x_2,\cdots, x_k}p_1^{x_1}p_2^{x_2}\cdots p_k^{x_k}</math>, where <math>x_1+x_2+\cdots+x_k=n</math>, <math>p_1+p_2+\cdots+p_k=1</math>, and <math>0 \le x_i \le n, 0 \le p_i \le 1</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/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/NegativeMultiNomial_Distribution.html Negative-Multinomial Binomial] PMF: <math> P(k_o, \cdots, k_r) = \Gamma(k_o + \sum_{i=1}^r{k_i}) \frac{p_o^{k_o}}{\Gamma(k_o)} \prod_{i=1}^r{\frac{p_i^{k_i}}{k_i!}} </math>
* [http://socr.ucla.edu/htmls/dist/Geometric_Distribution.html Geometric] PMF: <math> \begin{pmatrix} 1-p \end{pmatrix} ^{k-1}p  </math>
* [http://socr.ucla.edu/htmls/dist/Geometric_Distribution.html Geometric] PMF: <math> \begin{pmatrix} 1-p \end{pmatrix} ^{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/Erlang_Distribution.html Erlang] PDF: <math> \frac {\lambda x^{k-1}e^{-\lambda x}} {(k-1)!} </math>

Revision as of 05:29, 29 October 2009

Probability Density Functions (PDFs)

Transformations




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