I apologize if this should be asked elsewhere.

I have the following information:

enter image description here

Where N=1808

I am trying to calculate a given percentile (in this case p99.723), or ideally, if possible, generate data from this information. Unfortuneately, I do not have access to any further data, as this information is from a Journal article.

I'm running into trouble due to the extreme skewness of the distribution. Given the above information, I have the following questions:

  1. Is it possible to generate data from this information?
  2. If not (which I'm assuming I cannot), can I calculate the value for a given percentile (p99.723)?
  3. How can one do this? (I'm currently using Stata, but have access to Excel and am willing to do this by hand as well if needed).

Thank you in advance.

  • 1
    $\begingroup$ No - you have to make assumptions about the distributions and then try to shape them around the data. For example, at least $19$ institutions sent nothing in the year, and many more sent nothing on some days. You might try to derive that there could have been about $\frac{508.75\times 1808}{2580}\approx 356.5$ days in the year which is slightly strange, and might suggest day-of-the-week seasonality $\endgroup$
    – Henry
    May 14 at 16:46
  • $\begingroup$ @Henry, I'm assuming that your "no" response is to both questions (e.g. generate data or the p99.723 values), is that correct? Also, while I'd prefer to be as precise as possible, I am okay with making assumptions as this informtion would be used to inform further research questions, rather than inform the findings of research itself. $\endgroup$ May 14 at 17:00
  • 2
    $\begingroup$ Sure you can estimate percentiles from this information: but as @Henry points out, those estimates require making assumptions. Your estimates of the higher percentiles will be extremely sensitive to those assumptions! $\endgroup$
    – whuber
    May 14 at 18:09
  • $\begingroup$ @whuber, How can I go about estimating the percentiles from this? $\endgroup$ May 14 at 18:39
  • 1
    $\begingroup$ You assume a distribution family, fit a distribution, and use the percentiles of that distribution. I give an example at stats.stackexchange.com/a/276322/919 based on three percentiles. A mixture of percentiles and moment-based statistics is difficult to handle, because the likelihood is intractable, but one could use approximate methods to fit a distribution. The critical issue concerns your distributional assumption, because (for extreme percentiles) the answers depend even more on that than they do on the data! $\endgroup$
    – whuber
    May 14 at 19:55


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