# how to find standart devuation of biological data

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olga on 21 Aug 2013
I have biological data with big noise(see plot down). On this plot you can see several peaks, in my interest are two bigest of them. I want to find standart deviation of each of this peaks. Previously I used http://www.mathworks.com/matlabcentral/fileexchange/23452-interactive-peak-fitter-version-9-2 this function (Peak Fitter ) , but since I have biological data(very variable) this function doesn't work always. The algoritm which comes to my mind is next: 1)smooth and find peaks 2)cut peaks from each other manualy 3)fit them with gaussian 4)find standart deviation But I don't like to cut manualy this 2 peaks fron each other, I want to do it automaticaly but I don't know how it's possiable... May be someone knows how I can cut them automaticaly or have any ideas of alternative algoritm to find standart deviation

Jan on 21 Aug 2013
Edited: Jan on 21 Aug 2013
You could fit a Gaussian Mixture Model (GMM) with two Gaussians to the data using the Expectation Maximziation (EM-) Algorithm and extract the standard deviations from the result. Use findpeaks to initialize the mean values and start with small standard deviations. Applying a bandpass filter prior to this will definitely improve the result.
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Jan on 21 Aug 2013
Here you will find a very good description on how to do GMM fitting in Matlab.
In short call on your signal X
obj = gmdistribution.fit(X,k)
In your case, you would choose k=2 as you want to fit two Gaussians. The fitting results (mean and standard deviation) will be accessible in obj.mu and obj.Sigma, respectively. Look into the help file on how to set parameter initialization values.