Re: Name of a distribution.
- From: kunzmilan <kunzmilan@xxxxxxxx>
- Date: Thu, 02 Aug 2007 00:05:08 -0700
On 30 ec, 13:42, "Diamond, Mark" <d...@xxxxxxx> wrote:
I am looking for the name of a kind of distribution, or alternatively some
indication about how I would search for information on the distribution.
However, because I lack exactly that information, all I can do is describe
how to construct the distribution in which I'm interested.
So here goes ... first a rather poor generalization and then a specific
example.
If you allocate n marbles to n boxes, with the box for each of the n marbles
being chosen uniformly and at random from the n boxes, the what is the
"expected ranked allocation" of marbles in the boxes?
If I allocate three marbles to three boxes, they might be allocated {1,1,1},
with probability 2/9; {0,1,2}, {0,2,1}, {1,0,2}, {1,2,0}, {2,0,1}, {2,1,0},
*each* with probability 1/9; or {0,0,3}, {0,3,0}, {3,0,0}, each with
probability 1/27. Ignoring the permutations and looking at the triplets in
ascending rank order, I get {1,1,1) with probability 1/9, {0,1,2} with
probability 2/3 and {0,0,3} with probability 1/9. In some sense (whether it
is a nice sense or not, I don't know?) the expected rank ordered allocation
is {2/9, 8/9, 17/9} or instead, the normalized proportions are {0.222,
0.889, 1.889}.
Does that distribution have a standard name? If I want to know the similar
proportions for 100 marbles amongst 100 boxes, what distribution should I be
looking for? Answers to those questions or any other comments that might
help elucidate what I'm looking or draw my attention to parallel problems at
would be much appreciated.
Cheers,
Mark Diamond
Your problem is the base of combinatorics. The generating function (a
+ b + c)^3 gives 27 strigs. Between them 3 (aab, aba, baa). These are
reduced to a^2b, if you recognize only the number of marbles in boxes.
The partitions classify all strings as x^2y.
kunzmilan
.
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