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My program is a chatbot. It has rule to represent the state that user is talking to the bot at node level n. I have 1 to 9 nodes in the application. Here is the summary of each states

1    3331
2    695 
3    1381
4    945 
5    1754
6    5303
7    2235
8    1664
9    3844
Name: visited, dtype: int64

Last application state

If number 1 and 9 is not too high. I will not have a question.

Question:
Is it safe to call this distribution as a gaussian?

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    $\begingroup$ Not even close. $\endgroup$ Oct 16, 2018 at 13:30
  • $\begingroup$ How on earth can it be a Guassian when it isn't even a continuous distribution, its a discrete distribution on the integers 1 to 9? And asking "is it safe" is meaningless since we have no idea what inference you are going to make based on this distributional assumption. $\endgroup$
    – Spacedman
    Oct 17, 2018 at 8:05

1 Answer 1

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If you left out the large blue and yellow peaks, then maybe. Otherwise, no.

With all three distinct peaks, you might call it a multi-modal Guassian - meaning it is a mixture of three standard Gaussian distributions. This illustrates the idea:

Guassian mixture

Important: As pointed out by Spacedman in the comments, this comparison would only strictly apply if the data itself could be approximated as a continuous variable. This would mean you x-axis variable (state) should not be discrete. If the values were put in bins and your graph were therefore a histogram of the underlying data. Please have a look at this question for more details.


We can normally describe the distributions as being fat-tailed, when the extremes on the left and right of the curve don't ever really head towards zero, but seeing as your curve really shoots up again at both ends, I don't think it would be a useful description here.

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  • $\begingroup$ The data are both discrete and truncated so its nothing like a mixture of Gaussians, or Poisson. Please don't give bad statistical advice. $\endgroup$
    – Spacedman
    Oct 17, 2018 at 8:07
  • $\begingroup$ @Spacedman - agreed, I admit only answering visually. I have updated my answer. $\endgroup$
    – n1k31t4
    Oct 17, 2018 at 8:26
  • $\begingroup$ Also, look at the Y-axis. This plot comes from about 20,000 samples. If these were coming from N(a,b) and discretised then the uncertainty on those bars would be tiny, the histogram would look much more like a discretised Gaussian distribution. Maybe if this was from 200 or 100 samples you couldn't reject that hypothesis, but looking at this I can instantly say "This is not from a Gaussian distribution" (even ignoring the top and bottom bins). $\endgroup$
    – Spacedman
    Oct 17, 2018 at 10:04

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