# Generate given percentile (or data) from n, mean, median, standard deviation, p1, p25, p50, p75, p99?

I apologize if this should be asked elsewhere.

I have the following information:

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).

• 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 May 14 at 16:46