I have data from a heavy tailed distribution (see picture 1) and a non-heavy tailed distribution (see picture 2) and want to compare it using a histogram on log-scale. However the picture 3 does not really help because it does not resolve the different scales. I would also like to plot the mean and standard deviation using error bars. The notebook I used to generate these plots is available under notebook

Any suggestion is highly appreciated.

data 1

enter image description here

enter image description here

  • $\begingroup$ Personally, I'd consider the first distribution to have a heavier tail than the second precisely because of the difference in horizontal scale. $\endgroup$ – rcollyer Nov 12 '14 at 15:08
  • $\begingroup$ Based on a recent SIAM Review paper that looked at real world data, it's difficult to draw a boundary between exponential and power (empirical, ie observed) distributions. $\endgroup$ – alancalvitti Nov 12 '14 at 15:12
  • $\begingroup$ probably Skewness may help $\endgroup$ – molekyla777 Nov 12 '14 at 15:17
  • $\begingroup$ @rcollyer sorry the reference to pictures was wrong way round $\endgroup$ – warsaga Nov 12 '14 at 15:46
  • $\begingroup$ Histograms with the vertical axis on a log scale have never made much sense to me. (But they do tend to show up in this forum not infrequently.) And comparing moments (mean and standard deviations) for heavy tailed distributions (in part because for some heavy tailed distributions moments don't exist for the parent distribution even though on can calculate a moment for any particular sample) are rarely informative. $\endgroup$ – JimB Jun 10 '16 at 2:29

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