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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
d l
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  • If you think this comes from a negative binomial, you might try generating a bunch of samples from that negative binomial and seeing if their histograms have such bumps. – Michael Lugo Aug 29 '11 at 00:54

1 Answers1

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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.

Ross Millikan
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  • Thank you for the answer. "For a question like you cite" -- I see, I forgot to note random walk was an assumption, I've edited the question. This was real data collected in real life; it could be a random or non-random walk, I'm not sure which. – d l Aug 28 '11 at 21:56
  • @d l:If you are just looking at the data it is hard to decide whether it is a second bump or not. Many embarrassing moments in science are based on this. – Ross Millikan Aug 28 '11 at 22:39
  • thank you, this tells me how to interpret my "2nd bump", which it was I was looking for. – d l Aug 29 '11 at 00:06