Get the mean and standard deviation of the lower half of the first mode of a bimodal distribution

Hi, I have a bimodal distribution (in the form of a vector) from which I want to fit a gaussian distribution to the lower half of the first mode and calculate the mean and standard deviation of that distribution.

Any advice?

Answer 1

[Image Analyst]

Here is code that uses fitnlm() to fit two Gaussians, and one that fits multiple Gaussians.

[Stephen]

My Q doesn't apply to this specific thread (pls accept my apologies), but I don't know how else to contact Image Analyst. Some time back you helped out a user with a Q re: opening/closing an excel file from within MatLab. I'm having a devil of at time with the PlotInExcel function by Amit Doshi and am hoping you might shed some light. The problem is: I can't figure out how to save the file and quit Excel at the end of PlotInExcel. Consequently, I can't get back to my script. Excel just hangs open and I have to save/close it manually. Do you have any ideas? Any help would be greatly appreciated!

function PlotInExcel
   x= {1:10};
   a= cell2mat(x);
   y= {1:10};
   b= cell2mat(y);
   %............plotting..............................................................................................
   plot(a,b);
   xlabel('X Values');
   ylabel('Y Values');
   print -dmeta;   %.................Copying to clipboard

   FILE  = 'C:\DATA.xlsx';
   Range='OX14';
   %.............excel COM object............................................................................
         Excel = actxserver ('Excel.Application');
 Excel.Visible = 1;

 if ~exist(FILE,'file')
       ExcelWorkbook=Excel.Workbooks.Add;
       ExcelWorkbook.SaveAs(FILE);
       ExcelWorkbook.Close(false);
 end
 invoke(Excel.Workbooks,'Open',FILE); %Open the file
 ActiveSheet  = Excel.ActiveSheet;
 ActiveSheetRange  = get(ActiveSheet,'Range',Range);
 ActiveSheetRange.Select;
 ActiveSheetRange.PasteSpecial; %.................Pasting the figure to the selected location
 
%-----------------------------------end of function"PlotInExcel--------------------------------------
 

[Image Analyst]

Stephen, add these lines:

Excel.ActiveWorkbook.Save;
Excel.Quit;
delete(Excel);
clear('Excel')

See attached utilities for Excel.

Answer 2

[Abdolkarim Mohammadi]

You can first determine the elements that are in the lower half

LowerHalfMask = Data <= mean(Data);

Then calculate the statistics

LowerHalfMean = mean(Data(LowerHalfMask));
LowerHalfStd  = std(Data(LowerHalfMask));

To fit a distribution, you can first collect the elements of the lower half

LowerHalfValues = Data(LowerHalfMask);

Then use the Curve Fitting App (type cftool in the command window).

[Audun Kvalvaag]

Thanks, I solved it by mirroring the lower half of the first mode with the flip function. I could then use this gaussian fit function: https://www.mathworks.com/matlabcentral/fileexchange/35122-gaussian-fit to get the mean and standard deviation.