An alternative proof of a harmonic mean inequality for Nielsen’s beta function [PDF]
Contributions to Mathematics, 2021 Kwara Nantomah
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On the Bayesian interpretation of the harmonic mean p-value. [PDF]
Proc Natl Acad Sci U S A, 2019 Held L.
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The harmonic mean p-value: Strong versus weak control, and the assumption of independence. [PDF]
Proc Natl Acad Sci U S A, 2019 Goeman JJ, Rosenblatt JD, Nichols TE.
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The harmonic mean <i>p</i>-value for combining dependent tests. [PDF]
Proc Natl Acad Sci U S A, 2019 Wilson DJ.
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Reply to Held: When is a harmonic mean <i>p</i>-value a Bayes factor? [PDF]
Proc Natl Acad Sci U S A, 2019 Wilson DJ.
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We study the harmonic mean of non-zero complex-valued random variables (complex harmonic mean) and establish several geometric estimates and bounds. In contrast to the classical positive-valued case, complex harmonic means may lie outside the convex hull of the range. We prove that if the range is contained in a disk not containing the origin, then the
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Logarithmic mean and weighted sum of geometric and anti-harmonic means
Journal of Numerical Analysis and Approximation Theory, 2012 We consider the problem of finding the optimal values \(\alpha,\ \beta\in\mathbb{R}\) for which the inequality\[\alpha G(a,b)+(1-\alpha)C(a,b)
Mira Cristiana Anisiu, Valeriu Anisiu
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Comment on "Average Hazard as Harmonic Mean" by Chiba (2025). [PDF]
Pharm StatUno H, Tian L, Horiguchi M, Hattori S.
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Combining citation and productivity metrics through harmonic mean enhances researcher ranking accuracy. [PDF]
Sci RepMustafa G +5 more
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Deterministic and fractional-order modeling of measles dynamics with harmonic mean incidence rate and quarantine impact. [PDF]
Sci RepKhan R +4 more
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