I have the following problem:
I have an ordered list of $n$ data points jiggling around $0$ with no apparent order. The order this list is in should not be affected by the following procedure. I want to divide this list into 5 classes under the following conditions:
- Average of class no. 2 should be max. positive with variance the lower the better
- Average of class no. 4 should be max. negative with variance the lower the better
The average/variance of the other three classes doesn't matter at the moment.
How can I proceed optimizing the width/cutoff points of the 5 classes (some very crude tests support the belief that this should be possible in general)? Are the perhaps even implementations/tools for such tasks?
Is this problem known under some other name?