[R] Overlapping distributions (populations) - assigning an individual to a population?
Rolf Turner
r.turner at auckland.ac.nz
Wed Apr 9 00:57:39 CEST 2008
On 9/04/2008, at 10:30 AM, Phil Rhoades wrote:
> People,
>
> Say a particular measure of an attribute for individuals in different
> populations gives a set of overlapping normal distributions (one
> distribution per population). If I then measure this attribute in
> a new
> individual - how do I assess the likelihood of this new individual
> belonging to each of the different populations?
You have a mixture of distributions. Let the density be
k
f(x) = SUM lambda_i * f_i(x)
i=1
where the f_i(x) are the densities for the individual components in
the mixture,
and the lambda_i are the mixing probabilities.
The probability that an individual with observation x is from
component i is
lambda_i * f_i(x)
-----------------
f(x)
cheers,
Rolf Turner
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