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On the convergence of moments of geometric and harmonic means
Author(s) -
Pakes A. G.
Publication year - 1999
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00100
Subject(s) - mathematics , independent and identically distributed random variables , harmonic mean , moment (physics) , convergence (economics) , variance (accounting) , harmonic , random variable , statistics , mathematical analysis , econometrics , economics , physics , accounting , classical mechanics , quantum mechanics , economic growth
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.