R help - Aug 2008 - Fucntion scope question. General non-linear solution help.

I would like to solve the equation is is the sum from k = i to N of

choose(N,k) * MR ^ k * (1 - MR) ^ (N - k) - 0.50 = 0

I want to solve for MR. This seems like a non-linear equation to me. But I am
having a hard time writing the function that implements the above. I could use
'for(...) as a brute force appoarch but I would like a more
"elegant" solution. The variables 'N' and 'i' are
basically constant so the function has to take these from some kind of global
space. So if I take t brute force apporach I came up with:

f <- function(MR)
{
    k <- i:N
    return sum(choose(N,k) * MR ^ k * (1 - MR) ^ (N - k)) - 0.5
}

Does this seem like a reasonable implemetation? How are 'N' and
'i' declare as "global"? For each equation N and I are
constant but I want to be able to modify them. In other words solve the
equantion after setting N to 6 and i to 5 then again after setting i to 4.

The next question is regarding which 'R' function would be best suited
to solving this equation? I looked at 'nls' but that seems to take data
as an input. I want to solve the equation. What other options do I have? There
must be an 'R' function to solve a non-linear equation. I did
help.search("non-linear") and the closest match was nlm. But nlm
minimizes the function rather than solving it.

Ideas?

Thank you.

Kevin

Looks like you want to solve pbinom(k-1, N, p) = 0.5 for p.  That is easy: 
use uniroot.

testit <- function(k, N)
{
     fn <- function(p, k, N) pbinom(k-1, N, p) - 0.5
     uniroot(fn, c(0,1), k=k, N=N)
}
testit(6, 10)

On Sun, 17 Aug 2008, rkevinburton at charter.net wrote:
> I would like to solve the equation is is the sum from k = i to N of
>
> choose(N,k) * MR ^ k * (1 - MR) ^ (N - k) - 0.50 = 0
That's not what you have below: I presume that you want the sum to be 0.5.
The sum is 1 - pbinom(k-1, N, MR).
> I want to solve for MR. This seems like a non-linear equation to me. But I
am having a hard time writing the function that implements the above. I could
use 'for(...) as a brute force appoarch but I would like a more
"elegant" solution. The variables 'N' and 'i' are
basically constant so the function has to take these from some kind of global
space. So if I take t brute force apporach I came up with:
>
> f <- function(MR)
> {
>    k <- i:N
>    return sum(choose(N,k) * MR ^ k * (1 - MR) ^ (N - k)) - 0.5
> }
>
> Does this seem like a reasonable implemetation? How are 'N' and
'i' declare as "global"? For each equation N and I are
constant but I want to be able to modify them. In other words solve the
equantion after setting N to 6 and i to 5 then again after setting i to 4.
>
> The next question is regarding which 'R' function would be best
suited to solving this equation? I looked at 'nls' but that seems to
take data as an input. I want to solve the equation. What other options do I
have? There must be an 'R' function to solve a non-linear equation. I
did help.search("non-linear") and the closest match was nlm. But nlm
minimizes the function rather than solving it.
>
> Ideas?
>
> Thank you.
>
> Kevin
>
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>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
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