Gamma distribution (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Gamma distribution" in English language version.

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30doi.org

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ams.org

Choi, K. P. "On the Medians of the Gamma Distributions and an Equation of Ramanujan" Archived 2021-01-23 at the Wayback Machine, Proceedings of the American Mathematical Society, Vol. 121, No. 1 (May, 1994), pp. 245–251.

arxiv.org

Gopalan, Prem; Hofman, Jake M.; Blei, David M. (2013). "Scalable Recommendation with Poisson Factorization". arXiv:1311.1704 [cs.IR].
Berg, Christian and Pedersen, Henrik L. "Convexity of the median in the gamma distribution" Archived 2023-05-26 at the Wayback Machine.
Gaunt, Robert E., and Milan Merkle (2021). "On bounds for the mode and median of the generalized hyperbolic and related distributions". Journal of Mathematical Analysis and Applications. 493 (1): 124508. arXiv:2002.01884. doi:10.1016/j.jmaa.2020.124508. S2CID 221103640.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Lyon, Richard F. (13 May 2021). "On closed-form tight bounds and approximations for the median of a gamma distribution". PLOS One. 16 (5): e0251626. arXiv:2011.04060. Bibcode:2021PLoSO..1651626L. doi:10.1371/journal.pone.0251626. PMC 8118309. PMID 33984053.

biomedcentral.com

MA Mendoza-Parra, M Nowicka, W Van Gool, H Gronemeyer (2013) "Characterising ChIP-seq binding patterns by model-based peak shape deconvolution" Archived 2024-10-09 at the Wayback Machine, BMC Genomics, 14:834

books.google.com

Jessica., Scheiner, Samuel M., 1956- Gurevitch (2001). "13. Failure-time analysis". Design and analysis of ecological experiments. Oxford University Press. ISBN 0-19-513187-8. OCLC 43694448. Archived from the original on 2024-10-09. Retrieved 2022-05-26.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)

britannica.com

"Gamma distribution | Probability, Statistics, Distribution | Britannica". www.britannica.com. Archived from the original on 2024-05-19. Retrieved 2024-10-09.

devroye.org

luc.devroye.org

Devroye, Luc (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag. ISBN 978-0-387-96305-1. Archived from the original on 2012-07-17. Retrieved 2012-02-26. See Chapter 9, Section 3.

doi.org

Park, Sung Y.; Bera, Anil K. (2009). "Maximum entropy autoregressive conditional heteroskedasticity model" (PDF). Journal of Econometrics. 150 (2): 219–230. CiteSeerX 10.1.1.511.9750. doi:10.1016/j.jeconom.2008.12.014. Archived from the original (PDF) on 2016-03-07. Retrieved 2011-06-02.
Berg, Christian & Pedersen, Henrik L. (March 2006). "The Chen–Rubin conjecture in a continuous setting" (PDF). Methods and Applications of Analysis. 13 (1): 63–88. doi:10.4310/MAA.2006.v13.n1.a4. S2CID 6704865. Archived (PDF) from the original on 16 January 2021. Retrieved 1 April 2020.
Gaunt, Robert E., and Milan Merkle (2021). "On bounds for the mode and median of the generalized hyperbolic and related distributions". Journal of Mathematical Analysis and Applications. 493 (1): 124508. arXiv:2002.01884. doi:10.1016/j.jmaa.2020.124508. S2CID 221103640.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Lyon, Richard F. (13 May 2021). "On closed-form tight bounds and approximations for the median of a gamma distribution". PLOS One. 16 (5): e0251626. arXiv:2011.04060. Bibcode:2021PLoSO..1651626L. doi:10.1371/journal.pone.0251626. PMC 8118309. PMID 33984053.
Lyon, Richard F. (13 May 2021). "Tight bounds for the median of a gamma distribution". PLOS One. 18 (9): e0288601. doi:10.1371/journal.pone.0288601. PMC 10490949. PMID 37682854.
Mathai, A. M. (1982). "Storage capacity of a dam with gamma type inputs". Annals of the Institute of Statistical Mathematics. 34 (3): 591–597. doi:10.1007/BF02481056. ISSN 0020-3157. S2CID 122537756.
Moschopoulos, P. G. (1985). "The distribution of the sum of independent gamma random variables". Annals of the Institute of Statistical Mathematics. 37 (3): 541–544. doi:10.1007/BF02481123. S2CID 120066454.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (22 June 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme" (PDF). Communications in Statistics - Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587. Retrieved 2 September 2022.
Dubey, Satya D. (December 1970). "Compound gamma, beta and F distributions". Metrika. 16: 27–31. doi:10.1007/BF02613934. S2CID 123366328.
Choi, S. C.; Wette, R. (1969). "Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias". Technometrics. 11 (4): 683–690. doi:10.1080/00401706.1969.10490731.
Marsaglia, G.; Tsang, W. W. (2000). "A simple method for generating gamma variables". ACM Transactions on Mathematical Software. 26 (3): 363–372. doi:10.1145/358407.358414. S2CID 2634158.
Ye, Zhi-Sheng; Chen, Nan (2017). "Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 71 (2): 177–181. doi:10.1080/00031305.2016.1209129. S2CID 124682698. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Louzada, Francisco; Ramos, Pedro L.; Ramos, Eduardo (2019). "A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 73 (2): 195–199. doi:10.1080/00031305.2018.1513376. S2CID 126086375. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Vineyard, Michael; Amoako-Gyampah, Kwasi; Meredith, Jack R (July 1999). "Failure rate distributions for flexible manufacturing systems: An empirical study". European Journal of Operational Research. 116 (1): 139–155. doi:10.1016/s0377-2217(98)00096-4. ISSN 0377-2217. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Rief, Matthias; Rock, Ronald S.; Mehta, Amit D.; Mooseker, Mark S.; Cheney, Richard E.; Spudich, James A. (2000-08-15). "Myosin-V stepping kinetics: A molecular model for processivity". Proceedings of the National Academy of Sciences. 97 (17): 9482–9486. Bibcode:2000PNAS...97.9482R. doi:10.1073/pnas.97.17.9482. ISSN 0027-8424. PMC 16890. PMID 10944217.
Wilks, Daniel S. (1990). "Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros". Journal of Climate. 3 (12): 1495–1501. Bibcode:1990JCli....3.1495W. doi:10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2. ISSN 0894-8755. JSTOR 26196366.
Belikov, Aleksey V. (22 September 2017). "The number of key carcinogenic events can be predicted from cancer incidence". Scientific Reports. 7 (1): 12170. Bibcode:2017NatSR...712170B. doi:10.1038/s41598-017-12448-7. PMC 5610194. PMID 28939880.
Belikov, Aleksey V.; Vyatkin, Alexey; Leonov, Sergey V. (2021-08-06). "The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers". PeerJ. 9: e11976. doi:10.7717/peerj.11976. ISSN 2167-8359. PMC 8351573. PMID 34434669.
Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Ahrens, J. H.; Dieter, U (January 1982). "Generating gamma variates by a modified rejection technique". Communications of the ACM. 25 (1): 47–54. doi:10.1145/358315.358390. S2CID 15128188.. See Algorithm GD, p. 53.
Ahrens, J. H.; Dieter, U. (1974). "Computer methods for sampling from gamma, beta, Poisson and binomial distributions". Computing. 12 (3): 223–246. CiteSeerX 10.1.1.93.3828. doi:10.1007/BF02293108. S2CID 37484126.
Cheng, R. C. H.; Feast, G. M. (1979). "Some Simple Gamma Variate Generators". Journal of the Royal Statistical Society. Series C (Applied Statistics). 28 (3): 290–295. doi:10.2307/2347200. JSTOR 2347200.

dx.doi.org

Jeesen Chen, Herman Rubin, Bounds for the difference between median and mean of gamma and Poisson distributions, Statistics & Probability Letters, Volume 4, Issue 6, October 1986, Pages 281–283, ISSN 0167-7152, [1] Archived 2024-10-09 at the Wayback Machine.
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Vineyard, Michael; Amoako-Gyampah, Kwasi; Meredith, Jack R (July 1999). "Failure rate distributions for flexible manufacturing systems: An empirical study". European Journal of Operational Research. 116 (1): 139–155. doi:10.1016/s0377-2217(98)00096-4. ISSN 0377-2217. Archived from the original on 2024-10-09. Retrieved 2022-05-26.

elsevier.com

linkinghub.elsevier.com

Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.

figshare.com

Sun, Jingchao; Kong, Maiying; Pal, Subhadip (22 June 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme" (PDF). Communications in Statistics - Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587. Retrieved 2 September 2022.

harvard.edu

ui.adsabs.harvard.edu

Lyon, Richard F. (13 May 2021). "On closed-form tight bounds and approximations for the median of a gamma distribution". PLOS One. 16 (5): e0251626. arXiv:2011.04060. Bibcode:2021PLoSO..1651626L. doi:10.1371/journal.pone.0251626. PMC 8118309. PMID 33984053.
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Rief, Matthias; Rock, Ronald S.; Mehta, Amit D.; Mooseker, Mark S.; Cheney, Richard E.; Spudich, James A. (2000-08-15). "Myosin-V stepping kinetics: A molecular model for processivity". Proceedings of the National Academy of Sciences. 97 (17): 9482–9486. Bibcode:2000PNAS...97.9482R. doi:10.1073/pnas.97.17.9482. ISSN 0027-8424. PMC 16890. PMID 10944217.
Wilks, Daniel S. (1990). "Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros". Journal of Climate. 3 (12): 1495–1501. Bibcode:1990JCli....3.1495W. doi:10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2. ISSN 0894-8755. JSTOR 26196366.
Belikov, Aleksey V. (22 September 2017). "The number of key carcinogenic events can be predicted from cancer incidence". Scientific Reports. 7 (1): 12170. Bibcode:2017NatSR...712170B. doi:10.1038/s41598-017-12448-7. PMC 5610194. PMID 28939880.
Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.

intlpress.com

Berg, Christian & Pedersen, Henrik L. (March 2006). "The Chen–Rubin conjecture in a continuous setting" (PDF). Methods and Applications of Analysis. 13 (1): 63–88. doi:10.4310/MAA.2006.v13.n1.a4. S2CID 6704865. Archived (PDF) from the original on 16 January 2021. Retrieved 1 April 2020.

jstor.org

Wilks, Daniel S. (1990). "Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros". Journal of Climate. 3 (12): 1495–1501. Bibcode:1990JCli....3.1495W. doi:10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2. ISSN 0894-8755. JSTOR 26196366.
Cheng, R. C. H.; Feast, G. M. (1979). "Some Simple Gamma Variate Generators". Journal of the Royal Statistical Society. Series C (Applied Statistics). 28 (3): 290–295. doi:10.2307/2347200. JSTOR 2347200.

libretexts.org

stats.libretexts.org

"4.5: Exponential and Gamma Distributions". Statistics LibreTexts. 2019-03-11. Retrieved 2024-10-10.

nih.gov

pubmed.ncbi.nlm.nih.gov

Lyon, Richard F. (13 May 2021). "On closed-form tight bounds and approximations for the median of a gamma distribution". PLOS One. 16 (5): e0251626. arXiv:2011.04060. Bibcode:2021PLoSO..1651626L. doi:10.1371/journal.pone.0251626. PMC 8118309. PMID 33984053.
Lyon, Richard F. (13 May 2021). "Tight bounds for the median of a gamma distribution". PLOS One. 18 (9): e0288601. doi:10.1371/journal.pone.0288601. PMC 10490949. PMID 37682854.
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Rief, Matthias; Rock, Ronald S.; Mehta, Amit D.; Mooseker, Mark S.; Cheney, Richard E.; Spudich, James A. (2000-08-15). "Myosin-V stepping kinetics: A molecular model for processivity". Proceedings of the National Academy of Sciences. 97 (17): 9482–9486. Bibcode:2000PNAS...97.9482R. doi:10.1073/pnas.97.17.9482. ISSN 0027-8424. PMC 16890. PMID 10944217.
Belikov, Aleksey V. (22 September 2017). "The number of key carcinogenic events can be predicted from cancer incidence". Scientific Reports. 7 (1): 12170. Bibcode:2017NatSR...712170B. doi:10.1038/s41598-017-12448-7. PMC 5610194. PMID 28939880.
Belikov, Aleksey V.; Vyatkin, Alexey; Leonov, Sergey V. (2021-08-06). "The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers". PeerJ. 9: e11976. doi:10.7717/peerj.11976. ISSN 2167-8359. PMC 8351573. PMID 34434669.
Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.

ncbi.nlm.nih.gov

Lyon, Richard F. (13 May 2021). "On closed-form tight bounds and approximations for the median of a gamma distribution". PLOS One. 16 (5): e0251626. arXiv:2011.04060. Bibcode:2021PLoSO..1651626L. doi:10.1371/journal.pone.0251626. PMC 8118309. PMID 33984053.
Lyon, Richard F. (13 May 2021). "Tight bounds for the median of a gamma distribution". PLOS One. 18 (9): e0288601. doi:10.1371/journal.pone.0288601. PMC 10490949. PMID 37682854.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Rief, Matthias; Rock, Ronald S.; Mehta, Amit D.; Mooseker, Mark S.; Cheney, Richard E.; Spudich, James A. (2000-08-15). "Myosin-V stepping kinetics: A molecular model for processivity". Proceedings of the National Academy of Sciences. 97 (17): 9482–9486. Bibcode:2000PNAS...97.9482R. doi:10.1073/pnas.97.17.9482. ISSN 0027-8424. PMC 16890. PMID 10944217.
Belikov, Aleksey V. (22 September 2017). "The number of key carcinogenic events can be predicted from cancer incidence". Scientific Reports. 7 (1): 12170. Bibcode:2017NatSR...712170B. doi:10.1038/s41598-017-12448-7. PMC 5610194. PMID 28939880.
Belikov, Aleksey V.; Vyatkin, Alexey; Leonov, Sergey V. (2021-08-06). "The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers". PeerJ. 9: e11976. doi:10.7717/peerj.11976. ISSN 2167-8359. PMC 8351573. PMID 34434669.

probabilitycourse.com

"Gamma Distribution | Gamma Function | Properties | PDF". www.probabilitycourse.com. Archived from the original on 2024-06-13. Retrieved 2024-10-09.

psu.edu

citeseerx.ist.psu.edu

Park, Sung Y.; Bera, Anil K. (2009). "Maximum entropy autoregressive conditional heteroskedasticity model" (PDF). Journal of Econometrics. 150 (2): 219–230. CiteSeerX 10.1.1.511.9750. doi:10.1016/j.jeconom.2008.12.014. Archived from the original (PDF) on 2016-03-07. Retrieved 2011-06-02.
Fink, D. 1995 A Compendium of Conjugate Priors. In progress report: Extension and enhancement of methods for setting data quality objectives. (DOE contract 95‑831).
Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Ahrens, J. H.; Dieter, U. (1974). "Computer methods for sampling from gamma, beta, Poisson and binomial distributions". Computing. 12 (3): 223–246. CiteSeerX 10.1.1.93.3828. doi:10.1007/BF02293108. S2CID 37484126.

scipy.org

docs.scipy.org

"scipy.stats.loggamma — SciPy v1.8.0 Manual". docs.scipy.org.

semanticscholar.org

api.semanticscholar.org

Berg, Christian & Pedersen, Henrik L. (March 2006). "The Chen–Rubin conjecture in a continuous setting" (PDF). Methods and Applications of Analysis. 13 (1): 63–88. doi:10.4310/MAA.2006.v13.n1.a4. S2CID 6704865. Archived (PDF) from the original on 16 January 2021. Retrieved 1 April 2020.
Gaunt, Robert E., and Milan Merkle (2021). "On bounds for the mode and median of the generalized hyperbolic and related distributions". Journal of Mathematical Analysis and Applications. 493 (1): 124508. arXiv:2002.01884. doi:10.1016/j.jmaa.2020.124508. S2CID 221103640.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Mathai, A. M. (1982). "Storage capacity of a dam with gamma type inputs". Annals of the Institute of Statistical Mathematics. 34 (3): 591–597. doi:10.1007/BF02481056. ISSN 0020-3157. S2CID 122537756.
Moschopoulos, P. G. (1985). "The distribution of the sum of independent gamma random variables". Annals of the Institute of Statistical Mathematics. 37 (3): 541–544. doi:10.1007/BF02481123. S2CID 120066454.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (22 June 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme" (PDF). Communications in Statistics - Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587. Retrieved 2 September 2022.
Dubey, Satya D. (December 1970). "Compound gamma, beta and F distributions". Metrika. 16: 27–31. doi:10.1007/BF02613934. S2CID 123366328.
Marsaglia, G.; Tsang, W. W. (2000). "A simple method for generating gamma variables". ACM Transactions on Mathematical Software. 26 (3): 363–372. doi:10.1145/358407.358414. S2CID 2634158.
Ye, Zhi-Sheng; Chen, Nan (2017). "Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 71 (2): 177–181. doi:10.1080/00031305.2016.1209129. S2CID 124682698. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Louzada, Francisco; Ramos, Pedro L.; Ramos, Eduardo (2019). "A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 73 (2): 195–199. doi:10.1080/00031305.2018.1513376. S2CID 126086375. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Ahrens, J. H.; Dieter, U (January 1982). "Generating gamma variates by a modified rejection technique". Communications of the ACM. 25 (1): 47–54. doi:10.1145/358315.358390. S2CID 15128188.. See Algorithm GD, p. 53.
Ahrens, J. H.; Dieter, U. (1974). "Computer methods for sampling from gamma, beta, Poisson and binomial distributions". Computing. 12 (3): 223–246. CiteSeerX 10.1.1.93.3828. doi:10.1007/BF02293108. S2CID 37484126.

springer.com

link.springer.com

Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.

tandfonline.com

amstat.tandfonline.com

Ye, Zhi-Sheng; Chen, Nan (2017). "Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 71 (2): 177–181. doi:10.1080/00031305.2016.1209129. S2CID 124682698. Archived from the original on 2023-05-26. Retrieved 2019-07-27.

tandfonline.com

Louzada, Francisco; Ramos, Pedro L.; Ramos, Eduardo (2019). "A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 73 (2): 195–199. doi:10.1080/00031305.2018.1513376. S2CID 126086375. Archived from the original on 2023-05-26. Retrieved 2019-07-27.

tminka.github.io

Minka, Thomas P. (2002). "Estimating a Gamma distribution" (PDF).

ucl.ac.uk

fil.ion.ucl.ac.uk

Penny, W. D. "KL-Divergences of Normal, Gamma, Dirichlet, and Wishart densities".

web.archive.org

"Gamma distribution | Probability, Statistics, Distribution | Britannica". www.britannica.com. Archived from the original on 2024-05-19. Retrieved 2024-10-09.
Weisstein, Eric W. "Gamma Distribution". mathworld.wolfram.com. Archived from the original on 2024-05-28. Retrieved 2024-10-09.
"Gamma Distribution | Gamma Function | Properties | PDF". www.probabilitycourse.com. Archived from the original on 2024-06-13. Retrieved 2024-10-09.
Park, Sung Y.; Bera, Anil K. (2009). "Maximum entropy autoregressive conditional heteroskedasticity model" (PDF). Journal of Econometrics. 150 (2): 219–230. CiteSeerX 10.1.1.511.9750. doi:10.1016/j.jeconom.2008.12.014. Archived from the original (PDF) on 2016-03-07. Retrieved 2011-06-02.
Jeesen Chen, Herman Rubin, Bounds for the difference between median and mean of gamma and Poisson distributions, Statistics & Probability Letters, Volume 4, Issue 6, October 1986, Pages 281–283, ISSN 0167-7152, [1] Archived 2024-10-09 at the Wayback Machine.
Choi, K. P. "On the Medians of the Gamma Distributions and an Equation of Ramanujan" Archived 2021-01-23 at the Wayback Machine, Proceedings of the American Mathematical Society, Vol. 121, No. 1 (May, 1994), pp. 245–251.
Berg, Christian & Pedersen, Henrik L. (March 2006). "The Chen–Rubin conjecture in a continuous setting" (PDF). Methods and Applications of Analysis. 13 (1): 63–88. doi:10.4310/MAA.2006.v13.n1.a4. S2CID 6704865. Archived (PDF) from the original on 16 January 2021. Retrieved 1 April 2020.
Berg, Christian and Pedersen, Henrik L. "Convexity of the median in the gamma distribution" Archived 2023-05-26 at the Wayback Machine.
Ye, Zhi-Sheng; Chen, Nan (2017). "Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 71 (2): 177–181. doi:10.1080/00031305.2016.1209129. S2CID 124682698. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Louzada, Francisco; Ramos, Pedro L.; Ramos, Eduardo (2019). "A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations". The American Statistician. 73 (2): 195–199. doi:10.1080/00031305.2018.1513376. S2CID 126086375. Archived from the original on 2023-05-26. Retrieved 2019-07-27.
Jessica., Scheiner, Samuel M., 1956- Gurevitch (2001). "13. Failure-time analysis". Design and analysis of ecological experiments. Oxford University Press. ISBN 0-19-513187-8. OCLC 43694448. Archived from the original on 2024-10-09. Retrieved 2022-05-26.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Vineyard, Michael; Amoako-Gyampah, Kwasi; Meredith, Jack R (July 1999). "Failure rate distributions for flexible manufacturing systems: An empirical study". European Journal of Operational Research. 116 (1): 139–155. doi:10.1016/s0377-2217(98)00096-4. ISSN 0377-2217. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
DJ Reiss, MT Facciotti and NS Baliga (2008) "Model-based deconvolution of genome-wide DNA binding", Bioinformatics, 24, 396–403
MA Mendoza-Parra, M Nowicka, W Van Gool, H Gronemeyer (2013) "Characterising ChIP-seq binding patterns by model-based peak shape deconvolution" Archived 2024-10-09 at the Wayback Machine, BMC Genomics, 14:834
Yang, Ziheng (September 1996). "Among-site rate variation and its impact on phylogenetic analyses". Trends in Ecology & Evolution. 11 (9): 367–372. Bibcode:1996TEcoE..11..367Y. CiteSeerX 10.1.1.19.99. doi:10.1016/0169-5347(96)10041-0. PMID 21237881. Archived from the original on 2024-04-12. Retrieved 2023-09-06.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Devroye, Luc (1986). Non-Uniform Random Variate Generation. New York: Springer-Verlag. ISBN 978-0-387-96305-1. Archived from the original on 2012-07-17. Retrieved 2012-02-26. See Chapter 9, Section 3.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Gamma Distribution". mathworld.wolfram.com. Archived from the original on 2024-05-28. Retrieved 2024-10-09.

reference.wolfram.com

"ExpGammaDistribution—Wolfram Language Documentation".

worldcat.org

search.worldcat.org

Mathai, A. M. (1982). "Storage capacity of a dam with gamma type inputs". Annals of the Institute of Statistical Mathematics. 34 (3): 591–597. doi:10.1007/BF02481056. ISSN 0020-3157. S2CID 122537756.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (22 June 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme" (PDF). Communications in Statistics - Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587. Retrieved 2 September 2022.
Jessica., Scheiner, Samuel M., 1956- Gurevitch (2001). "13. Failure-time analysis". Design and analysis of ecological experiments. Oxford University Press. ISBN 0-19-513187-8. OCLC 43694448. Archived from the original on 2024-10-09. Retrieved 2022-05-26.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)
Golubev, A. (March 2016). "Applications and implications of the exponentially modified gamma distribution as a model for time variabilities related to cell proliferation and gene expression". Journal of Theoretical Biology. 393: 203–217. Bibcode:2016JThBi.393..203G. doi:10.1016/j.jtbi.2015.12.027. ISSN 0022-5193. PMID 26780652. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Poon, Art; Davis, Bradley H; Chao, Lin (2005-07-01). "The Coupon Collector and the Suppressor Mutation". Genetics. 170 (3): 1323–1332. doi:10.1534/genetics.104.037259. ISSN 1943-2631. PMC 1451182. PMID 15879511. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Vineyard, Michael; Amoako-Gyampah, Kwasi; Meredith, Jack R (July 1999). "Failure rate distributions for flexible manufacturing systems: An empirical study". European Journal of Operational Research. 116 (1): 139–155. doi:10.1016/s0377-2217(98)00096-4. ISSN 0377-2217. Archived from the original on 2024-10-09. Retrieved 2022-05-26.
Rief, Matthias; Rock, Ronald S.; Mehta, Amit D.; Mooseker, Mark S.; Cheney, Richard E.; Spudich, James A. (2000-08-15). "Myosin-V stepping kinetics: A molecular model for processivity". Proceedings of the National Academy of Sciences. 97 (17): 9482–9486. Bibcode:2000PNAS...97.9482R. doi:10.1073/pnas.97.17.9482. ISSN 0027-8424. PMC 16890. PMID 10944217.
Wilks, Daniel S. (1990). "Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros". Journal of Climate. 3 (12): 1495–1501. Bibcode:1990JCli....3.1495W. doi:10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2. ISSN 0894-8755. JSTOR 26196366.
Belikov, Aleksey V.; Vyatkin, Alexey; Leonov, Sergey V. (2021-08-06). "The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers". PeerJ. 9: e11976. doi:10.7717/peerj.11976. ISSN 2167-8359. PMC 8351573. PMID 34434669.
Yang, Ziheng (September 1994). "Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods". Journal of Molecular Evolution. 39 (3): 306–314. Bibcode:1994JMolE..39..306Y. CiteSeerX 10.1.1.19.6626. doi:10.1007/BF00160154. ISSN 0022-2844. PMID 7932792. S2CID 17911050. Archived from the original on 2024-10-09. Retrieved 2023-09-06.
Felsenstein, Joseph (2001-10-01). "Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies". Journal of Molecular Evolution. 53 (4–5): 447–455. Bibcode:2001JMolE..53..447F. doi:10.1007/s002390010234. ISSN 0022-2844. PMID 11675604. S2CID 9791493. Archived from the original on 2024-10-09. Retrieved 2023-09-06.

worldcat.org

Jeesen Chen, Herman Rubin, Bounds for the difference between median and mean of gamma and Poisson distributions, Statistics & Probability Letters, Volume 4, Issue 6, October 1986, Pages 281–283, ISSN 0167-7152, [1] Archived 2024-10-09 at the Wayback Machine.
Jessica., Scheiner, Samuel M., 1956- Gurevitch (2001). "13. Failure-time analysis". Design and analysis of ecological experiments. Oxford University Press. ISBN 0-19-513187-8. OCLC 43694448. Archived from the original on 2024-10-09. Retrieved 2022-05-26.{{cite book}}: CS1 maint: multiple names: authors list (link) CS1 maint: numeric names: authors list (link)

xmu.edu.cn

wise.xmu.edu.cn

Park, Sung Y.; Bera, Anil K. (2009). "Maximum entropy autoregressive conditional heteroskedasticity model" (PDF). Journal of Econometrics. 150 (2): 219–230. CiteSeerX 10.1.1.511.9750. doi:10.1016/j.jeconom.2008.12.014. Archived from the original (PDF) on 2016-03-07. Retrieved 2011-06-02.