where wu and of are the mean and variance of y = In x, respectively. Finney %1941) derived a minimum variance unbiased estimator (MVUF) for EX because of the large bias of the maximum likelihood estimator (MLE). Finney's estimator is E(x) = exp(¥) 8, (8/2) where y is the arithmetic mean of the log transformed x values, s? is the variance of the log transformed x values, and the function g is the infinite series g(t) =l1+ (n-1)t + (n-1) >t? n + no(nt1)2! (n-1)°t? n> (ntl) (n43)3! +... A finite sample confidence interval can be estimated for E(x) by Cox's directmethod (Land, 1972). A confidence interval is calculated for the value y + 1/2 s* and then antiloged to achieve an interval on E(x). This interval ig asymmetric, but has the desirable property that the lower confidence bound cannot be negative. Cox’s direct method was shown to be easily the best of the approximate methods considered by Land and was recommended by him when dealing with large sample sizes and moderate values of s*, Land's exact method is not used because of the computational diffictlties involved. Estimation of the EX for the gamma distribution is much simpler than for the lognormal distribution. The EX of the gamma distribution is the product of the parameters a and 8, where the probability density function is f (x) = x T (a) 8” exp (-x/B) xo dx (x > 0; a > 0, The maximum likelihood equations to estimate ao and 8 are Wette, 1969) A ¥(a)} + log B = y 8 > Q) (Choi and UA , anda gp=x where Y(t) is the psi (diagamma) function. Hence we see by the invari- ance property_of MLE's that x is the MLE of FX for the gamma distribution. In addition, x is also an MVUE of EX. This result is known because (1) the gamma distribution is a member of the exponential family, (2) the set of minimal sufficient statistics (MSS) is 612