Tight bounds for the median of a gamma distribution

Richard F Lyon

PLOS ONE, 2023, vol. 18, issue 9, 1-18

Abstract: The median of a standard gamma distribution, as a function of its shape parameter k, has no known representation in terms of elementary functions. In this work we prove the tightest upper and lower bounds of the form 2−1/k(A + k): an upper bound with A = e−γ (with γ being the Euler–Mascheroni constant) and a lower bound with A = log ( 2 ) - 1 3. These bounds are valid over the entire domain of k > 0, staying between 48 and 55 percentile. We derive and prove several other new tight bounds in support of the proofs.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0288601

DOI: 10.1371/journal.pone.0288601

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