 If "X" is a positive random variable and "q" > 0 then for all "ε" > 0

Assuming that "X" and E("X") are > 0 then

This follows from Jensen's inequality.Gurland has shown that for a distribution that takes only positive values, for any "n" > 0

Under some conditions

where ~ means approximately.Assuming that the variates ("x") are drawn from a lognormal distribution there are several possible estimators for "H"