Re: Looking for a distribution
- From: iandjmsmith@xxxxxxx
- Date: 30 Aug 2006 07:54:24 -0700
junk6@xxxxxxxxxxxxxxxx wrote:
Hi
My r.v. is a vector, B, of binary values (0 or 1) of finite length (N,
say). The probability of the i-th element of the vector being a 1 is
p_i (i.e. each element element of the vector may have a different pmf).
Given an observation (i.e. a vector of 0s and 1s), I'm interested in
the sum of the vector (i.e. the number of 1s).
I'm looking for an approach that allows one to determine the
probability of the sum being a given value on [0, N]. I can see how to
construct the distribution by brute force (see next paragraph), but is
there a better approach?
If the vector has two elements, I can construct a 2x2 table with the
possible sums (0, 1, 1 and 2) and easily compute the probabilities of
the sums 0,1 and 2. If the vector has three elements, the table needs
to be a 3-D array. So in general for a N-vector we require the
computation of 2^N probabilities (and then some tidying up after the
multiple entries for the same sum).
Is there a general solution? Does it generalise to the case where
elements of B come from some finite set (i.e. not just 0 and 1); or
where the elements of B are real values with pdfs?
Thanks in advance
C
See
http://groups.google.co.uk/group/sci.math/browse_frm/thread/38bc9330921e80e0/
I have some VBA code for the calculations, if you are interested.
Ian Smith
.
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