# What is a good way to deal with finite trains from random variables?

EDIT:

Disregard this question if it is formulated too confusing. This link provides you with the updated version of the same question What is the most powerful test for process discrimination based on its finite output?

EDIT>

It's a general question, about dealing with randomness on finite trains. I have two finite and not very big strings of numbers. Each of them comes from one of two possible random variables.

I need to discriminate between the situation where the strings come from the same random variable from the case where they are result of two different random variables. I do it on the the basis of my finite strings.

The problem is that the difference of the random variables is not very big. One can not certainly say from which of variables the string has come from.

Is there any possibility to enhance the prediction?

Simple example:

Say, I have two Gaussian variables with different mean and same variance. When I produce a set of trials from them and plot their distributions, they look like two close bells. Is there a method that can give me a more reliable answer.

![two Gaussian distributions]

For example: If I square all values in the set of trials the variance gets smaller and the bells get more distinguishable.

But at the same time I enhance any fluctuations and noise and I can get a false positive.

![two Gaussian distributions squared]

Can't post pictures as a new user. Here are links.

http://i.stack.imgur.com/GK7VM.png

http://i.stack.imgur.com/0yqkW.png

-
This may get better answers at the statistics StackExchange. – Rahul Nov 20 '12 at 17:50
Thank you. I've asked there as well. – neuronich Nov 20 '12 at 17:58