التفاصيل البيبلوغرافية
| العنوان: |
Tight bounds for the median of a gamma distribution. |
| المؤلفون: |
Lyon, Richard F.1 (AUTHOR) dicklyon@acm.org |
| المصدر: |
PLoS ONE. 9/8/2023, Vol. 18 Issue 9, p1-18. 18p. |
| مصطلحات موضوعية: |
*GAMMA distributions, *MEDIAN (Mathematics) |
| مستخلص: |
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)-13. 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. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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