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I'm a chain store and have many stores across the country that all sell a particular shampoo product P.

I have made a plot as shown in the image below. For example, 30 stores each sold 1 of P in the past two weeks. The sum of the areas of the bars is the total number of P sold across all stores in the past two weeks.

What should be the theoretical shape of this plot? You may assume anything that gives a clean answer to this.

Sales

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    $\begingroup$ This question is somewhat unclear, it would be helpful to see what your graph actually looks like - is it some form of histogram? I'm not sure that "the theoretical distribution of product sales" is an answerable question. $\endgroup$ – Silverfish Aug 18 '16 at 11:12
  • $\begingroup$ Maybe Log-normal or Poisson distribution? You should perform statisitcal test for distribution. $\endgroup$ – fl0r3k Aug 18 '16 at 12:54
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    $\begingroup$ Ultimately this is a question about how stores sell shampoo: it is not a question that statistics can legitimately answer, since there is no theory of shampoo sales in stores. I won't deny that statistical ideas can shed light on this issue, so I will vote to reopen; but I would like to suggest that you change your question to focus on whatever your analytical objective might be so that you don't get sidetracked by such irrelevant and possibly misleading issues. $\endgroup$ – whuber Aug 18 '16 at 13:39
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    $\begingroup$ "You may assume anything that gives a clean answer to this" is not something you should encourage. There are going to be assumptions that lead to mutually exclusive "clean answers". Given that someone stipulates one of them, how will you know if it's relevant to your situation or if the answer is worse that useless & takes you down the wrong path. $\endgroup$ – gung - Reinstate Monica Aug 18 '16 at 15:45
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    $\begingroup$ What would "statistically natural" mean? Since there is no statistical theory of shampoo sales, it's difficult to translate that phrase into anything that can be analyzed. What we do know is that sales depend on store size, visibility, retail catchment area, pricing, surrounding demographics, local demand, advertising, and much more. This distribution (and distributions of other products) reflect variation in those factors. If you wish to make any inferences about this particular product then you need to control for such factors. $\endgroup$ – whuber Aug 19 '16 at 12:34

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