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I have to solve this at work.
- There are N individuals. N is unknown (thousands).
- There are M groups. M is known (hundreds).
- All individuals belong at least to 1 group, at most to K groups. K is
known (tens).
- The exact number of individuals L for each group is known. It ranges from
1 to several hundreds.
- The proportion P of how many individuals belong to a certain number of
groups is known. For instance, we know that 50% of the individuals belong to
only one group, 20% belong to 2 groups and so on.
- We have sampled the population for 12 of the larger groups and found that
the ratio of [actual size of the population belonging to the 12 groups]/[sum
of the population sizes (L) for the 12 groups] to be 80%.
With all the parameters above, it possible to estimate the size of N?
Of course, the maximum estimate is sum(L). Empirically, I'd say that a
better estimate is 0.8 x sum(L), but I have the (also empirical) feeling
that the actual number is much, much lower.
(The real-life problem deals with bibliometry: individuals are scientific
articles and groups are keywords.)
G.
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de news: 47f49de8@news.povray.org...
>I have to solve this at work.
Never mind, I found the solution... It wasn't that difficult but as usual,
having to explain a problem is the best way to really think about it.
Basically, the sum of the M group sizes sum(L) is equal to sum(N*Pj*j) where
j is a number of groups and Pj the percentage of individuals belonging to j
groups.
So we have sum(L)=sum(N*Pj*j) = N*sum(Pj*j) so N= sum(L)/sum(Pj*j)
G.
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Gilles Tran wrote:
> de news: 47f49de8@news.povray.org...
>> I have to solve this at work.
>
> Never mind, I found the solution... It wasn't that difficult but as usual,
> having to explain a problem is the best way to really think about it.
Ah. The famous DBTAI! (Debugging by talking about it)
This explains the phenomenon of colleagues coming up and telling you in
immense detail about a problem and then leaving, before you have a
chance to say a word, saying "Thanks very much for the help."
John
--
I will be brief but not nearly so brief as Salvador Dali, who gave the
world's shortest speech. He said, "I will be so brief I am already
finished," then he sat down.
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On Thu, 03 Apr 2008 19:56:55 +0100, Doctor John <doc### [at] gmail com> wrote:
>Ah. The famous DBTAI! (Debugging by talking about it)
>This explains the phenomenon of colleagues coming up and telling you in
>immense detail about a problem and then leaving, before you have a
>chance to say a word, saying "Thanks very much for the help."
I do that to my wife all the time. She's non-technical, but she'll sit and listen to
me drone on about electronics or programming projects, she'll sit and watch me draw
elaborate diagrams on paper
napkins at the spur of the moment, all without saying much of anything except
"mmm-hmm" when she feels it's appropriate. It sure helps me figure things out
sometimes, even though she provides no
input. Then again, I'm sure she's afraid to ask me to elaborate on any points she
doesn't comprehend.
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Kyle wrote:
> I do that to my wife all the time. She's non-technical, but she'll sit and listen
to me drone on about electronics or programming projects, she'll sit and watch me draw
elaborate diagrams on paper
> napkins at the spur of the moment, all without saying much of anything except
"mmm-hmm" when she feels it's appropriate. It sure helps me figure things out
sometimes, even though she provides no
> input. Then again, I'm sure she's afraid to ask me to elaborate on any points she
doesn't comprehend.
Heh. It's a bit like that when I talk to my mum. [The only human being I
reguarly speak to.] Except that half way through she'll say "so it's
like..." and proceed to describe a long and intricate metaphore which is
either unecessarily detailed to explain such a simple concept, or is
wildly incorrect, tangental to what I was saying, or doesn't make sense.
Damn it, I need a wife... :-S
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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> I do that to my wife all the time. She's non-technical, but she'll sit
> and listen to me drone on about electronics or programming projects,
> she'll sit and watch me draw elaborate diagrams on paper
> napkins at the spur of the moment, all without saying much of anything
> except "mmm-hmm" when she feels it's appropriate.
You should feel lucky, my gf says "ok that's enough" after about 3 sentences
of anything remotely technical!
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