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## Main Question or Discussion Point

Hi! I have some measurements of the rate of a physical process versus energy. For each energy I have a number of counts and a measurement time associated to it. However, the step (in energy) at which the measurements are made is very small and also the measurement time is small, hence just plotting a rate vs energy for each measured energy doesn't really work (many energy entries also have zero counts).

I would like to bin the data such that to obtain a reasonable shape of the spectrum for a fit (I also have something of the order 10,000 measurements, so doing directly a log-likelihood would not work). Assuming that the error on the x axis (energy) is negligible and the errors are Poisson, how should I choose the right bin size?

Also, how should I choose the x and y for each bin (to use for the fit)? For the y, I think the right way to do is to add all the counts in that bin (N) and all the measuring time (T) and give the rate (y value) as N/T with the error ##\sqrt{N}/T##. For x axis, I could just use the average of the energy values in that bin. However, for some energies the measuring time is higher than for others. Should I use a time weighted average in order to get the x of the bin? Should I just use the center of the bin?

Thank you!

I would like to bin the data such that to obtain a reasonable shape of the spectrum for a fit (I also have something of the order 10,000 measurements, so doing directly a log-likelihood would not work). Assuming that the error on the x axis (energy) is negligible and the errors are Poisson, how should I choose the right bin size?

Also, how should I choose the x and y for each bin (to use for the fit)? For the y, I think the right way to do is to add all the counts in that bin (N) and all the measuring time (T) and give the rate (y value) as N/T with the error ##\sqrt{N}/T##. For x axis, I could just use the average of the energy values in that bin. However, for some energies the measuring time is higher than for others. Should I use a time weighted average in order to get the x of the bin? Should I just use the center of the bin?

Thank you!