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 May 24th, 2015, 06:18 AM #1 Newbie   Joined: Nov 2013 Posts: 19 Thanks: 0 Seeking approximation method of a probability expression. Dear all, Given: $P^R_n(i) = \beta ^ \left( i-m \right) ( 1 - \beta ) ^ \left( n-i+m \right) \binom{n-m}{i-m}$ and $\phi$ Want: $I^{min} _n = min \{ j: \sum_{i=j}^n P^R_n(i) < \phi \}$ I mean if there exists any simple ways of approximating or calculating the result of $\sum_{i=j}^n P^R_n(i)$. Or approximating $\sum_{i=j}^n P^R_n(i)$ withgut multiplying one after one of the multipliers of the factorial.
 May 24th, 2015, 03:13 PM #2 Global Moderator   Joined: May 2007 Posts: 6,754 Thanks: 695 Your statement is somewhat confusing. What role does m have in $\displaystyle P_n^R(i)$?
 May 24th, 2015, 07:06 PM #3 Newbie   Joined: Nov 2013 Posts: 19 Thanks: 0 $m$ is also a given number less than $n$.
May 24th, 2015, 07:31 PM   #4
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 Originally Posted by rubis Dear all, Given: $P^R_n(i) = \beta ^ \left( i-m \right) ( 1 - \beta ) ^ \left( n-i+m \right) \binom{n-m}{i-m}$ and $\phi$ Want: $I^{min} _n = min \{ j: \sum_{i=j}^n P^R_n(i) < \phi \}$ I mean if there exists any simple ways of approximating or calculating the result of $\sum_{i=j}^n P^R_n(i)$. Or approximating $\sum_{i=j}^n P^R_n(i)$ withgut multiplying one after one of the multipliers of the factorial.

I mean if there exists any simple ways of approximating or calculating the result of $\sum_{i=j}^n P^R_n(i)$.
Or approximating $\binom{n-m}{i-m}$ without multiplying one after one multipliers of the factorial.

 May 24th, 2015, 08:42 PM #5 Newbie   Joined: Nov 2013 Posts: 19 Thanks: 0 I think this website has been hacked, because I have found someone had modified my message!

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