What algorithms can be used to characterize an expected clearly bimodal distribution, say a mixture of 2 normal distributions with well separated peaks, in an array of samples? Something that spits out 2 means, 2 standard deviations, and some sort of robustness estimate, would be the desired result.
I am interested in an algorithm that can be implemented in any programming language (for an embedded controller), not an existing C or Python library or stat package.
Would it be easier if I knew that the two modal means differ by a ratio of approximately 3:1 +- 50%, the standard deviations are “small” relative to the peak separation, but the pair of peaks could be anywhere in a 100:1 range?
There are two separate possibilities here. One is that you have a single distribution that is bimodal. The other is that you are observing data from two different distributions. The usual way to estimate the later is in something called, unsurprisingly, a mixture model.
Your approaches for estimating are to use a maximum likelihood approach or use Markov chain Monte Carlo methods if you want to take a Bayesian view of the problem. If you state your assumptions in a bit more detail I’d be willing to help try and figure out what objective function you’d want to try and maximize.
These type of models can be computationally intensive, so I am not sure you’d want to try and do the whole statistical approach in an embedded controller. A hack might be a better fit. If the peaks are in fact well separated, I think it would be easier to try and identify the two peaks and split your data between them and do the estimation of the mean and standard deviation for each distribution independently.