# [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

######################################################################
Attention:\ This e-mail message is privileged and confid...{{dropped:9}}

```