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Summary For positive‐valued random variables, the paper provides a sequence of upper bounds for the harmonic mean, the i th of these bounds being exact if and only if the random variable is essentially i ‐valued. Sufficient conditions for the convergence of the bounds to the harmonic mean are given. The bounds have a number of applications, particularly in experimental design where they may be used to check how close a given design is to A ‐optimality
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Fitzpatrick et al. (1986) studied this question.
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