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, [EMAIL PROTECTED] 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, [EMAIL PROTECTED]
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)
Oxford OX1 3TG, UK Fax: +44 1865 272595
______________________________________________
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