Dan Esperantos wrote in
news:[EMAIL PROTECTED]:
> Your help in this problem is highly appreciated.
>
> Suppose we are given a multinomial probability distribution
> N!
snipped out an expression mucked up by word wrap
>
> How to compute an approximation of the following
> probability, where {X_i}s are distributed as above:
>
> P( X_1 = max{X_1, X_2,..., X_K} )?
>
> if p>q or if p > q*(K-1)
>
> For example, when K=2 we simply have (assume N is even):
> N N!
> P( X_1 = max{X_1, X_2} ) = P( X_1 >= X_2 ) = Sum -------- p^i*(1-p)^(N-i)
> i=N/2 i!(N-i)!
>
> Are any approximations known for such sums?
> What about the case of general K?
> In my applications N is on order of several hundreds,
> so exact computation is not feasible.
>
I haven't checked your logic, but that summation looks like
a right tail probability for the negative binomial.
There are good approximations for N! that should work if
you want to roll your own function, but there is a multitude
of canned functions out on the Web.
--
David Winsemius
If the statistics are boring, then you've got the wrong numbers.
-Edward Tufte
.
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