How to bin data logarithmically and assign errors for fitting

[NoobixCube]

Hey all,

I have a bunch of data that varies over many magnitudes. I was hoping to use log bins to capture the short and long term features of the data. My question is, how do I bin the data, and how do I assign appropriate errors so that I can fit the data to some theory (maybe a power law)?

Cheers!

 

[Redbelly98]

Probably the most straightforward method is to rescale the data as y=log₁₀(x), and then take equal intervals in binning the y data.

Good question about the errors. I'm not absolutely sure, but I believe that the error would be ± the square root of the expected number of counts within a bin, at least when that count total is considerably greater than 1. This becomes problematic when the expected count is less than 1, for example 0.25±0.5 allows for negative counts, an unphysical result.

Perhaps somebody who knows statistics better than I can provide a more accurate answer.

 

[NoobixCube]

Hey Redbelly98,

thanks for your reply :) I will look into it and post back with results.

 

[NoobixCube]

I have managed to find this website with MATLAB scripts relevant to my initial query, that may help people in the future who are asking the same, or a similar question:

http://www-personal.umich.edu/~ladamic/courses/si614w06/matlab/index.html

 

[NoobixCube]

I have managed to find this website with MATLAB scripts relevant to my initial query, that may help people in the future who are asking the same, or a similar question:

http://www-personal.umich.edu/~ladamic/courses/si614w06/matlab/index.html

Also,

I have modified the scripts on the page given in my previous reply, and uploaded a MATLAB file to MATLAB Central

http://www.mathworks.com/matlabcentral/fileexchange/27176-log-binning-of-data