5
$\begingroup$

Using JMP, I was able to fit a distribution to a set of data, using the normal-2 mixtures model. It returns location (or mean), dispersion (standard deviation) and probability for each of the two normal distributions used to create the normal-2 mixtures. Now, I want to be able to take any data point from that population, and figure out the odds that data point came from each of the two distributions. Is there a way to do this?

$\endgroup$
  • 2
    $\begingroup$ I can write JMP scripting code or SQL or something else to calculate the values if I have the formulas involved. $\endgroup$ – cwyers May 16 '14 at 19:32
4
$\begingroup$

Let's call the estimates from population 1 and population 2 to be

$\mu_1$ and $\mu_2$ for the means, $\sigma_1$ and $\sigma_2$ for the sd's. Also, let's define $p$ to be the estimated proportion of observations from population 1.

Then, for each observation $x_i$, the estimated probability of belonging to population 1 is

$= \dfrac{p*N( x_i ; \mu_1, \sigma_1)}{p*N( x_i ; \mu_1, \sigma_1) +(1-p)*N( x_i ; \mu_2, \sigma_2)}$

where $N( x_i ; \mu_1, \sigma_1)$ is the normal density. If using JMP, you could evaluate the normal density with

Normal.Density( (x_i - mu_1) / sigma_1) )

since the normal density function in JMP only accepts arguments for the standard normal distribution.

The estimated probability of belonging to population 2 would then of course be 1 minus the estimated probability of belonging to population 1.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.