Is there a way to estimate harmonic mean given other statistics such as arithmetic mean, variance, min, max, ... .

The goal is to estimate the mean incrementally as we get new data using a few counters.

  • $\begingroup$ You can use the AM-GM -HM inequality to get an upper bound. $\endgroup$ – Alex R. May 29 '18 at 23:37
  • $\begingroup$ Unfortunately, the GM bound is too loose in practical cases. Is there a way to augment it with something that improves the bound? $\endgroup$ – Masood_mj May 29 '18 at 23:49
  • $\begingroup$ No, there isn't. Unless, you have more information about your data. $\endgroup$ – Alex R. May 30 '18 at 0:33
  • $\begingroup$ The HM cannot be below the minimum, so that's one possible lower bound. There are some additional bounds around that relate to these quantities, but if you want to do better than fairly weak bounds you'll probably need to supply more information about the variable in some way. $\endgroup$ – Glen_b May 30 '18 at 3:21
  • $\begingroup$ Thanks Alex. Glen, can you please give examples? Like what statistics would be useful and how? $\endgroup$ – Masood_mj May 30 '18 at 3:45

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