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I've plotted a histogram of data collected in real life, not generated data. It looks like a negative binomial binomial distribution with a 2nd bump, lower from the peak bump of the curve. Here is a screenshot: negative binomial with 2 bumps

Question - is the second bump of any significance? Is it expected and not significant, as if produced expected to be produced by chance? Or does it indicate something, like 2 populations in my sample data?

Notes:

  • Sample size - 21,700;
  • Question as "In a random walk, on average, how many steps does it take to move a distance of 10 steps from the starting position?" -- but the random walk is assumed, the process that generated my data could be a non-random walk
  • Uneven spacing due to most counts are even numbers
  • did not do a qqplot to verify what kind of distribution, negative binomial is a guess
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    If $y$ou think this comes from a negative binomial, $y$ou might tr$y$ generating a bunch of samples from that negative binomial and seeing if their histograms have such bumps.2011-08-29

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For a question like you cite, I don't see where a second bump would come from. Another way to characterize your histogram is a dip around $59$. It could be a problem in the way you generate the random numbers, or it could be a statistical fluctuation. If you have a theoretical curve, you could check the chi-square.

If it is a 1 dimensional random walk, all the counts should be even, so you should make sure there are the same number of even numbers in each bin.

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    thank you, this tells me how to interpret my "2nd bump", which it was I was looking for.2011-08-29