Hassan Tehranian, Billy P. Helms, An Empirical Comparison of Stochastic Dominance among Lognormal Prospects, The Journal of Financial and Quantitative Analysis, Vol. 17, No. 2 (Jun., 1982), pp. 217-226

In 1959, Henry Lataná [2] proposed an approximation to the geometric mean that was a simple function of the arithmetic mean and variance, thereby indicating a mathematical relationship between the risky investment choice model of Bernoulli and the Markowitz mean-variance model. In 1969, Young and Trent [4] presented empirical test results of the Latané approximation, as well as a set of other approximations to the geometric mean based on moments, and concluded that the Latane formula yielded a quite accurate approximation to the geometric mean. In Jean's 1980 paper [1] relating the geometric mean model to stochastic dominance models, the infinite series representation of the geometric mean used suggests a more accurate approximation with moments of the geometric mean than that contained in the earlier papers may be possible. Various forms of that series expressed in alternate-origin moments are tested empirically below, and the results confirm that this later series does yield the greatest accuracy of the three approaches.