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I have large sample of data that is approximately from a Pareto distribution with unknown parameters. Unfortunately the distribution is sufficiently heavy tailed that just taking the sample mean is not a good estimate. What is a good way to estimate the mean and variance in this case?

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    $\begingroup$ Because it's only "approximately" Pareto, and the quality of any procedure relying on such a distributional assumption is likely to be strongly sensitive to departures from being exactly Pareto, it would be difficult to suggest an objective solution. Because the sample is large, why wouldn't the sample mean be good? "Large" and "good" in what senses, specifically? $\endgroup$
    – whuber ♦
    Commented Jul 26, 2023 at 20:29
  • $\begingroup$ @whuber The problem with the sample mean can be seen by reporting the mean every time $10^6$ values are summed. The mean changes quite a lot when rare but large values are encountered. $\endgroup$
    – Simd
    Commented Jul 26, 2023 at 20:32
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    $\begingroup$ The problem is evident, but you haven't yet supplied any information to let us assess how big it might be or to identify likely alternative estimators. $\endgroup$
    – whuber ♦
    Commented Jul 26, 2023 at 20:33
  • $\begingroup$ @whuber what sort of information would be useful? My sample is of size 10 million. $\endgroup$
    – Simd
    Commented Jul 26, 2023 at 20:39
  • $\begingroup$ Do you really need to estimate the mean and variance of your sample or could another notion and scale (e.g. median and median absolute deviation) be of use ? $\endgroup$
    – Pohoua
    Commented Jul 26, 2023 at 21:04

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