placing data into which distribution?

[distribution]

Hello all,

I have two sets of data, which are divided by a single category.

I want to be able to place further observations into one of these distributions, and put a confidence level on which distribution the data falls in.

The problem is that I only understand how to do this for normal distributions, where the usual confidence intervals and t statistics hold. How would I do this for two distributions that are heavily skewed.

The distributions have different means, and are clearly different.

How would I place probabilities on which distributions further data observations lie (where I do not observe their category)?

I was thinking about simply using, observation x has value 10, in distribution 1 10% of values lie between 9 and 11, and in distriubtion 2, 20% of the values lie within this range. Therefore there is a 66% chance the observation is in distribution 2. Is this the right idea approximately?

Thanks for the help,

I am excited to hear your responses,

Thanks!

[Dason]

You could consider using Bayes theorem?