On the convergence of moments of geometric and harmonic means

A. G. Pakes

Statistica Neerlandica, 1999, vol. 53, issue 1, 96-110

Abstract: The moments of the geometric mean of n independent and identically distributed random variables are shown to converge as n→∞. Rates of convergence are determined for the first moment and the variance. The results relate to recent work on long term investment returns when yearly rates of return are randomly varying. Application is made to moments of the harmonic mean.

Date: 1999
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