Approximation of the expected value of the harmonic mean and some applications.
other · Level V
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- Record sourced from PubMed, PMID 25331886.
- Also identified by DOI 10.1073/pnas.1412216111 and PMC identifier 4226087.
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Abstract
Although the harmonic mean (HM) is mentioned in textbooks along with the arithmetic mean (AM) and the geometric mean (GM) as three possible ways of summarizing the information in a set of observations, its appropriateness in some statistical applications is not mentioned in textbooks. During the last 10 y a number of papers were published giving some statistical applications where HM is appropriate and provides a better performance than AM. In the present paper some additional applications of HM are considered. The key result is to find a good approximation to [Formula: see text], the expectation of the harmonic mean of n observations from a probability distribution. In this paper a second-order approximation to [Formula: see text] is derived and applied to a number of problems.