GEOMETRIC MEAN FOR NEGATIVE AND ZERO VALUES

A geometric mean tends to dampen the effect of very high values where it is a log-transformation of data. In this paper, the geometric mean for data that includes negative and zero values are derived. It turns up that the data could have one geometric mean, two geometric means or three geometric means. Consequently, the geometric mean for discrete distributions is obtained. The concept of geometric unbiased estimator is introduced and the interval estimation for the geometric mean is studied in terms of coverage probability. It is shown that the geometric mean is more efficient than the median in the estimation of the scale parameter of the log-logistic distribution.