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How one can describe correctly the procedure of making a histogram. I want to replace the sentence "distributions of reconstructed energies of events taken with the same initial momentum in the same test-beam experiment are fitted..." into two sentences: one for describing the "histogram making" and the second to describe the fitting method.

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    Seems to me that this is more of a math question. – Hot Licks Aug 24 '18 at 12:03
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If you are fitting a parametric distribution to observed data,this typically means finding the values of the parameters where the distribution “most closely matches” the histogram.

Practically speaking, however, the distribution is assumed, and a formula is applied to the data with the help of a computer program. The parameters are calculated, along with a “goodness of fit” number that you use to decide whether the distribution matches the data. The histogram never appears explicitly, although most statistical programs offer some way to visualize histograms and fitted distributions.

From your very brief text, it looks like you want to describe the fitting process as if it were being done in a simple way, as in an exercise in an introductory statistics course. There’s nothing wrong with this, and it might be entirely appropriate for your readers, but it might be better to describe the histogram as a visualization output as opposed to an intermediate variable in the analysis.

For example:

  • Each experiment yielded a set of reconstructed energies, which could in principle be plotted as histograms on a common set of axes.

  • A ________ distribution was fitted to each of the sets.

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