Formulas

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(Probability Density Functions (PDFs))
(Probability Density Functions (PDFs))
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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>
* [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>
* [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  
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* [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)} \cr ,  
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* [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) ,  
P(X=x)={1\over x!} \left[{\partial ^{x-1} \over \partial z^{x-1} } \left\{(g(z))^{x} {\partial f(z)\over \partial z} \right\}\right]_{z=0}  ,    x>0</math> Where f(z) and g(z) are pgf  ,  <math>\left[{\partial ^{x-1} \over \partial z^{x-1} } \left\{(g(z))^{x} {\partial f(z)\over \partial z} \right\}\right]_{z=0} >0</math> for <math>x\ge 1</math>
P(X=x)={1\over x!} \left[{\partial ^{x-1} \over \partial z^{x-1} } \left\{(g(z))^{x} {\partial f(z)\over \partial z} \right\}\right]_{z=0}  ,    x>0</math> Where f(z) and g(z) are pgf  ,  <math>\left[{\partial ^{x-1} \over \partial z^{x-1} } \left\{(g(z))^{x} {\partial f(z)\over \partial z} \right\}\right]_{z=0} >0</math> for <math>x\ge 1</math>
* [http://socr.ucla.edu/htmls/dist/Binomial-delta_Distribution.html Binomial-delta distribution]: <math> P(X=x)={n\over x}\binom{{mx}}{x-n}p^{x-n} q^{n+mx-x} </math>  for  <math>x\ge n</math>
* [http://socr.ucla.edu/htmls/dist/Binomial-delta_Distribution.html Binomial-delta distribution]: <math> P(X=x)={n\over x}\binom{{mx}}{x-n}p^{x-n} q^{n+mx-x} </math>  for  <math>x\ge n</math>

Revision as of 12:46, 18 January 2011

Probability Density Functions (PDFs)

         where    x = 1,2,...,n

Transformations






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