Formulas

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(Probability Density Functions (PDFs))
(Probability Density Functions (PDFs))
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* [http://socr.ucla.edu/htmls/dist/Lévy_Distribution.html Lévy distribution]: <math> L_{\alpha ,\gamma } (y)={1\over \pi } \int _{0}^{\infty }e^{-\gamma q^{\alpha } } \cos (qy) dq    ,            y\in {\rm R} , \gamma >0 , 0<\alpha <2  </math>
* [http://socr.ucla.edu/htmls/dist/Lévy_Distribution.html Lévy distribution]: <math> L_{\alpha ,\gamma } (y)={1\over \pi } \int _{0}^{\infty }e^{-\gamma q^{\alpha } } \cos (qy) dq    ,            y\in {\rm R} , \gamma >0 , 0<\alpha <2  </math>
* [http://socr.ucla.edu/htmls/dist/Modified-Power-Series_Distribution.html Modified Power Series distributon]: <math> P(X=x)={a(x)\left\{u(c)\right\}^{x} \over A(c)}    </math>  where  <math> A(c)=\sum _{x}a(x)\left\{u(c)\right\}^{x}  ,a(x)\ge 0 </math>
* [http://socr.ucla.edu/htmls/dist/Modified-Power-Series_Distribution.html Modified Power Series distributon]: <math> P(X=x)={a(x)\left\{u(c)\right\}^{x} \over A(c)}    </math>  where  <math> A(c)=\sum _{x}a(x)\left\{u(c)\right\}^{x}  ,a(x)\ge 0 </math>
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* [http://socr.ucla.edu/htmls/dist/Positive-binomial_Distribution.html Positive binomial distribution]: <math> P(X=x)=\left\binom{n}{x}\right{p^{x} q^{n-x} \over (1-q^{n} )} </math>          where    <math>  x=1,2,...,n </math>
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* [http://socr.ucla.edu/htmls/dist/Positive-binomial_Distribution.html Positive binomial distribution]: <math> P(X=x)=\binom{n}{x}{p^{x} q^{n-x} \over (1-q^{n} )} </math>          where    <math>  x=1,2,...,n </math>
* [http://socr.ucla.edu/htmls/dist/Basic-Lagrangian-distribution-of-the-first-kind.html Basic Lagrangian distribution of the first kind (BLD1)]: <math> P(X=x)={1\over x!} \left[{\partial ^{x-1} \over \partial z^{x-1} } (g(z))^{x} \right]_{z=0} </math>  where <math>  g(z) </math> is pgf , <math> g(0) </math> is not 0  
* [http://socr.ucla.edu/htmls/dist/Basic-Lagrangian-distribution-of-the-first-kind.html Basic Lagrangian distribution of the first kind (BLD1)]: <math> P(X=x)={1\over x!} \left[{\partial ^{x-1} \over \partial z^{x-1} } (g(z))^{x} \right]_{z=0} </math>  where <math>  g(z) </math> is pgf , <math> g(0) </math> is not 0  
* [http://socr.ucla.edu/htmls/dist/General-Basic-Lagrangian-distribution-of-the-first-kind.html General Basic Lagrangian distribution of the first kind (GLD1)]: <math> P(X=0)=f(0) ,  
* [http://socr.ucla.edu/htmls/dist/General-Basic-Lagrangian-distribution-of-the-first-kind.html General Basic Lagrangian distribution of the first kind (GLD1)]: <math> P(X=0)=f(0) ,  

Revision as of 12:55, 18 January 2011

Probability Density Functions (PDFs)

Transformations






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