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Suppose I have a large population, in the millions, drawn from some underlying distribution, which we will take as a member of a known distributional family with unknown parameters. Assume the population is ordered along some variable of interest. In addition to the common statistics usually reported on large populations, the agency that collected the data has provided the sum of, say, the top hundredth of a percent of the population, or, say, the top 500 households.

Should I analyse this in terms the underlying distribution, for example as a conditional mean? Or as a a sum of order statistics? Or do I need to use some extension of the extreme value distribution?

My ultimate goal is to determine the parameters of the underlying population distribution, one of which is primarily specific to the upper tail.

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  • $\begingroup$ I came across the same problem a while back. Figured out some ad hoc stuff, but no great solution. $\endgroup$ Feb 25 at 13:59
  • $\begingroup$ Will you specify the distributional family and the available statistics? From your description, you might be estimating a shifted log-normal from the mean, the standard deviation, and the average of the top percentile -- that would be straightforward, but you probably have more parameters and more data. $\endgroup$
    – Matt F.
    Mar 1 at 15:02

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