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I am trying to estimate measured signal, which has multimodal behaviour, usually 1-3 modes (see trimodal sample frequencies below for example), but in one experimental setup it's 1, 2 or 3 all the time.

trimodal example frequencies time series

First of all, I need to confirm this can be modelled as a mix of Gaussians (as some research from the problem domain hints, but I am slightly sceptical before I check my data). The underlying physics of the process is multi-path propagation of the signal, so different measurements may be from different paths (there are other effects, but this seems to be the strongest). My concern is there are not many different values for that (and sample size may also be limited to a thousands).

And more important, how to get the estimate of the mode with highest value (NB. they are negative).

My approach is to use weighted sum for the 5 highest values (by frequency) as it simple to calculate in the iterative manner (when needed in dynamic case).

Update: to the very least, will it be too wrong to just ignore measurements after second negative peak like -94 and try to fit those to normal distribution (or maybe Rayleigh)?

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  • $\begingroup$ If you sometimes get 1 mode, sometimes 2, sometimes 3 then the first thing to consider is how stable the modality is and how far it is an artefact of the measurement or reporting process. Jumping towards mixture modelling seems a little premature. I am not especially surprised at minor modes in a sample of 367 when (from the evidence here) the number of possible values is quite small. Is the variable continuous in principle or discrete in principle (I guess the former, but please confirm)? $\endgroup$ – Nick Cox Dec 10 '15 at 9:20
  • $\begingroup$ Added time series chart. Variable is continuous, measured value is quantized a lot. Modes are clearly seen on longer samples, they are no artefact. In this particular case there was some disturbance at the beginning, but otherwise it is quite stable. $\endgroup$ – Roman Susi Dec 10 '15 at 9:28
  • $\begingroup$ Also "sometimes" is across similar, but different experiments. In one experiment the picture is usually the same. $\endgroup$ – Roman Susi Dec 10 '15 at 11:19

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