Poisson distribution (English Wikipedia)

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

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actuaries.org.uk

Clarke, R. D. (1946). "An application of the Poisson distribution" (PDF). Journal of the Institute of Actuaries. 72 (3): 481. doi:10.1017/S0020268100035435.

arxiv.org

Helske, Jouni (2017). "KFAS: Exponential Family State Space Models in R". Journal of Statistical Software. 78 (10). arXiv:1612.01907. doi:10.18637/jss.v078.i10. S2CID 14379617.
D. Ahle, Thomas (2022). "Sharp and simple bounds for the raw moments of the Binomial and Poisson distributions". Statistics & Probability Letters. 182: 109306. arXiv:2103.17027. doi:10.1016/j.spl.2021.109306.
Kamath, Govinda M.; Şaşoğlu, Eren; Tse, David (14–19 June 2015). Optimal haplotype assembly from high-throughput mate-pair reads. 2015 IEEE International Symposium on Information Theory (ISIT). Hong Kong, China. pp. 914–918. arXiv:1502.01975. doi:10.1109/ISIT.2015.7282588. S2CID 128634.
Dytso, Alex; Poor, H. Vincent (2020). "Estimation in Poisson noise: Properties of the conditional mean estimator". IEEE Transactions on Information Theory. 66 (7): 4304–4323. arXiv:1911.03744. doi:10.1109/TIT.2020.2979978. S2CID 207853178.

bnf.fr

gallica.bnf.fr

Poisson, Siméon D. (1837). Probabilité des jugements en matière criminelle et en matière civile, précédées des règles générales du calcul des probabilités [Research on the Probability of Judgments in Criminal and Civil Matters] (in French). Paris, France: Bachelier.

books.google.com

de Moivre, Abraham (1718). The Doctrine of Chances: Or, A Method of Calculating the Probability of Events in Play. London, Great Britain: W. Pearson. ISBN 9780598843753.
Cameron, A. Colin; Trivedi, Pravin K. (1998). Regression Analysis of Count Data. Cambridge, UK: Cambridge University Press. ISBN 978-0-521-63567-7.

cnx.org

Paszek, Ewa. "Maximum likelihood estimation – examples". cnx.org.

devroye.org

luc.devroye.org

Devroye, Luc (1986). "Discrete Univariate Distributions" (PDF). Non-Uniform Random Variate Generation. New York, NY: Springer-Verlag. pp. 485–553. doi:10.1007/978-1-4613-8643-8_10. ISBN 978-1-4613-8645-2.

doi.org

de Moivre, Abraham (1711). "De mensura sortis, seu, de probabilitate eventuum in ludis a casu fortuito pendentibus" [On the Measurement of Chance, or, on the Probability of Events in Games Depending Upon Fortuitous Chance]. Philosophical Transactions of the Royal Society (in Latin). 27 (329): 213–264. doi:10.1098/rstl.1710.0018.
Johnson, Norman L.; Kemp, Adrienne W.; Kotz, Samuel (2005). "Poisson Distribution". Univariate Discrete Distributions (3rd ed.). New York, NY, US: John Wiley & Sons, Inc. pp. 156–207. doi:10.1002/0471715816. ISBN 978-0-471-27246-5.
Stigler, Stephen M. (1982). "Poisson on the Poisson Distribution". Statistics & Probability Letters. 1 (1): 33–35. doi:10.1016/0167-7152(82)90010-4.
Hald, Anders; de Moivre, Abraham; McClintock, Bruce (1984). "A. de Moivre: 'De Mensura Sortis' or 'On the Measurement of Chance'". International Statistical Review / Revue Internationale de Statistique. 52 (3): 229–262. doi:10.2307/1403045. JSTOR 1403045.
Dekking, Frederik Michel; Kraaikamp, Cornelis; Lopuhaä, Hendrik Paul; Meester, Ludolf Erwin (2005). A Modern Introduction to Probability and Statistics. Springer Texts in Statistics. p. 167. doi:10.1007/1-84628-168-7. ISBN 978-1-85233-896-1.
Helske, Jouni (2017). "KFAS: Exponential Family State Space Models in R". Journal of Statistical Software. 78 (10). arXiv:1612.01907. doi:10.18637/jss.v078.i10. S2CID 14379617.
Choi, Kwok P. (1994). "On the medians of gamma distributions and an equation of Ramanujan". Proceedings of the American Mathematical Society. 121 (1): 245–251. doi:10.2307/2160389. JSTOR 2160389.
Riordan, John (1937). "Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions" (PDF). Annals of Mathematical Statistics. 8 (2): 103–111. doi:10.1214/aoms/1177732430. JSTOR 2957598.
D. Ahle, Thomas (2022). "Sharp and simple bounds for the raw moments of the Binomial and Poisson distributions". Statistics & Probability Letters. 182: 109306. arXiv:2103.17027. doi:10.1016/j.spl.2021.109306.
von Mises, Richard (1964). Mathematical Theory of Probability and Statistics. New York, NJ, US: Academic Press. doi:10.1016/C2013-0-12460-9. ISBN 978-1-4832-3213-3.
Harremoes, P. (July 2001). "Binomial and Poisson distributions as maximum entropy distributions". IEEE Transactions on Information Theory. 47 (5): 2039–2041. doi:10.1109/18.930936. S2CID 16171405.
Short, Michael (2013). "Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions". ISRN Probability and Statistics. 2013. Corollary 6. doi:10.1155/2013/412958.
Short, Michael (2013). "Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions". ISRN Probability and Statistics. 2013. Theorem 2. doi:10.1155/2013/412958.
Kamath, Govinda M.; Şaşoğlu, Eren; Tse, David (14–19 June 2015). Optimal haplotype assembly from high-throughput mate-pair reads. 2015 IEEE International Symposium on Information Theory (ISIT). Hong Kong, China. pp. 914–918. arXiv:1502.01975. doi:10.1109/ISIT.2015.7282588. S2CID 128634.
Zhang, Huiming; Liu, Yunxiao; Li, Bo (2014). "Notes on discrete compound Poisson model with applications to risk theory". Insurance: Mathematics and Economics. 59: 325–336. doi:10.1016/j.insmatheco.2014.09.012.
Zhang, Huiming; Li, Bo (2016). "Characterizations of discrete compound Poisson distributions". Communications in Statistics - Theory and Methods. 45 (22): 6789–6802. doi:10.1080/03610926.2014.901375. S2CID 125475756.
Anscombe, Francis J. (1948). "The transformation of Poisson, binomial and negative binomial data". Biometrika. 35 (3–4): 246–254. doi:10.1093/biomet/35.3-4.246. JSTOR 2332343.
Loukas, Sotirios; Kemp, C. David (1986). "The Index of Dispersion Test for the Bivariate Poisson Distribution". Biometrics. 42 (4): 941–948. doi:10.2307/2530708. JSTOR 2530708.
Garwood, Frank (1936). "Fiducial Limits for the Poisson Distribution". Biometrika. 28 (3/4): 437–442. doi:10.1093/biomet/28.3-4.437. JSTOR 2333958.
Dytso, Alex; Poor, H. Vincent (2020). "Estimation in Poisson noise: Properties of the conditional mean estimator". IEEE Transactions on Information Theory. 66 (7): 4304–4323. arXiv:1911.03744. doi:10.1109/TIT.2020.2979978. S2CID 207853178.
Clevenson, M. Lawrence; Zidek, James V. (1975). "Simultaneous estimation of the means of independent Poisson laws". Journal of the American Statistical Association. 70 (351): 698–705. doi:10.1080/01621459.1975.10482497. JSTOR 2285958.
Berger, James O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer Series in Statistics (2nd ed.). New York, NY: Springer-Verlag. Bibcode:1985sdtb.book.....B. doi:10.1007/978-1-4757-4286-2. ISBN 978-0-387-96098-2.
Rasch, Georg (1963). The Poisson Process as a Model for a Diversity of Behavioural Phenomena (PDF). 17th International Congress of Psychology. Vol. 2. Washington, DC: American Psychological Association. doi:10.1037/e685262012-108.
Flory, Paul J. (1940). "Molecular Size Distribution in Ethylene Oxide Polymers". Journal of the American Chemical Society. 62 (6): 1561–1565. doi:10.1021/ja01863a066.
a student (1907). "On the error of counting with a haemacytometer". Biometrika. 5 (3): 351–360. doi:10.2307/2331633. JSTOR 2331633.
Boland, Philip J. (1984). "A biographical glimpse of William Sealy Gosset". The American Statistician. 38 (3): 179–183. doi:10.1080/00031305.1984.10483195. JSTOR 2683648.
Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu (2016). "Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation". Food Microbiology. 60: 49–53. doi:10.1016/j.fm.2016.05.019. PMID 27554145.
Clarke, R. D. (1946). "An application of the Poisson distribution" (PDF). Journal of the Institute of Actuaries. 72 (3): 481. doi:10.1017/S0020268100035435.
Hardy, Godfrey H.; Littlewood, John E. (1923). "On some problems of "partitio numerorum" III: On the expression of a number as a sum of primes". Acta Mathematica. 44: 1–70. doi:10.1007/BF02403921.
Gallagher, Patrick X. (1976). "On the distribution of primes in short intervals". Mathematika. 23 (1): 4–9. doi:10.1112/s0025579300016442.
Edgeworth, F.Y. (1913). "On the use of the theory of probabilities in statistics relating to society". Journal of the Royal Statistical Society. 76 (2): 165–193. doi:10.2307/2340091. JSTOR 2340091.
Katz, B.; Miledi, R. (August 1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology. 224 (3): 665–699. doi:10.1113/jphysiol.1972.sp009918. ISSN 0022-3751. PMC 1331515. PMID 5071933.
Foster, Patricia L. (1 January 2006), "Methods for Determining Spontaneous Mutation Rates", Methods in Enzymology, DNA Repair, Part B, 409, Academic Press: 195–213, doi:10.1016/S0076-6879(05)09012-9, ISBN 978-0-12-182814-1, PMC 2041832, PMID 16793403
Devroye, Luc (1986). "Discrete Univariate Distributions" (PDF). Non-Uniform Random Variate Generation. New York, NY: Springer-Verlag. pp. 485–553. doi:10.1007/978-1-4613-8643-8_10. ISBN 978-1-4613-8645-2.

dx.doi.org

Katz, B.; Miledi, R. (August 1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology. 224 (3): 665–699. doi:10.1113/jphysiol.1972.sp009918. ISSN 0022-3751. PMC 1331515. PMID 5071933.

harvard.edu

ui.adsabs.harvard.edu

Berger, James O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer Series in Statistics (2nd ed.). New York, NY: Springer-Verlag. Bibcode:1985sdtb.book.....B. doi:10.1007/978-1-4757-4286-2. ISBN 978-0-387-96098-2.

hathitrust.org

babel.hathitrust.org

Newcomb, Simon (1860). "Notes on the theory of probabilities". The Mathematical Monthly. 2 (4): 134–140.

iarc.fr

Breslow, Norman E.; Day, Nick E. (1987). Statistical Methods in Cancer Research. Vol. 2 — The Design and Analysis of Cohort Studies. Lyon, France: International Agency for Research on Cancer. ISBN 978-92-832-0182-3. Archived from the original on 8 August 2018. Retrieved 11 March 2012.

jstor.org

Hald, Anders; de Moivre, Abraham; McClintock, Bruce (1984). "A. de Moivre: 'De Mensura Sortis' or 'On the Measurement of Chance'". International Statistical Review / Revue Internationale de Statistique. 52 (3): 229–262. doi:10.2307/1403045. JSTOR 1403045.
Choi, Kwok P. (1994). "On the medians of gamma distributions and an equation of Ramanujan". Proceedings of the American Mathematical Society. 121 (1): 245–251. doi:10.2307/2160389. JSTOR 2160389.
Riordan, John (1937). "Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions" (PDF). Annals of Mathematical Statistics. 8 (2): 103–111. doi:10.1214/aoms/1177732430. JSTOR 2957598.
Anscombe, Francis J. (1948). "The transformation of Poisson, binomial and negative binomial data". Biometrika. 35 (3–4): 246–254. doi:10.1093/biomet/35.3-4.246. JSTOR 2332343.
Loukas, Sotirios; Kemp, C. David (1986). "The Index of Dispersion Test for the Bivariate Poisson Distribution". Biometrics. 42 (4): 941–948. doi:10.2307/2530708. JSTOR 2530708.
Garwood, Frank (1936). "Fiducial Limits for the Poisson Distribution". Biometrika. 28 (3/4): 437–442. doi:10.1093/biomet/28.3-4.437. JSTOR 2333958.
Clevenson, M. Lawrence; Zidek, James V. (1975). "Simultaneous estimation of the means of independent Poisson laws". Journal of the American Statistical Association. 70 (351): 698–705. doi:10.1080/01621459.1975.10482497. JSTOR 2285958.
a student (1907). "On the error of counting with a haemacytometer". Biometrika. 5 (3): 351–360. doi:10.2307/2331633. JSTOR 2331633.
Boland, Philip J. (1984). "A biographical glimpse of William Sealy Gosset". The American Statistician. 38 (3): 179–183. doi:10.1080/00031305.1984.10483195. JSTOR 2683648.
Erlang, Agner K. (1909). "Sandsynlighedsregning og Telefonsamtaler" [Probability Calculation and Telephone Conversations]. Nyt Tidsskrift for Matematik (in Danish). 20 (B): 33–39. JSTOR 24528622.
Edgeworth, F.Y. (1913). "On the use of the theory of probabilities in statistics relating to society". Journal of the Royal Statistical Society. 76 (2): 165–193. doi:10.2307/2340091. JSTOR 2340091.

nih.gov

pubmed.ncbi.nlm.nih.gov

Koyama, Kento; Hokunan, Hidekazu; Hasegawa, Mayumi; Kawamura, Shuso; Koseki, Shigenobu (2016). "Do bacterial cell numbers follow a theoretical Poisson distribution? Comparison of experimentally obtained numbers of single cells with random number generation via computer simulation". Food Microbiology. 60: 49–53. doi:10.1016/j.fm.2016.05.019. PMID 27554145.
Katz, B.; Miledi, R. (August 1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology. 224 (3): 665–699. doi:10.1113/jphysiol.1972.sp009918. ISSN 0022-3751. PMC 1331515. PMID 5071933.
Foster, Patricia L. (1 January 2006), "Methods for Determining Spontaneous Mutation Rates", Methods in Enzymology, DNA Repair, Part B, 409, Academic Press: 195–213, doi:10.1016/S0076-6879(05)09012-9, ISBN 978-0-12-182814-1, PMC 2041832, PMID 16793403

ncbi.nlm.nih.gov

Katz, B.; Miledi, R. (August 1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology. 224 (3): 665–699. doi:10.1113/jphysiol.1972.sp009918. ISSN 0022-3751. PMC 1331515. PMID 5071933.
Foster, Patricia L. (1 January 2006), "Methods for Determining Spontaneous Mutation Rates", Methods in Enzymology, DNA Repair, Part B, 409, Academic Press: 195–213, doi:10.1016/S0076-6879(05)09012-9, ISBN 978-0-12-182814-1, PMC 2041832, PMID 16793403

nist.gov

itl.nist.gov

Prins, Jack (2012). "6.3.3.1. Counts Control Charts". e-Handbook of Statistical Methods. NIST/SEMATECH. Retrieved 20 September 2019.

projecteuclid.org

Riordan, John (1937). "Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions" (PDF). Annals of Mathematical Statistics. 8 (2): 103–111. doi:10.1214/aoms/1177732430. JSTOR 2957598.

proofwiki.org

For the proof, see: Proof wiki: expectation and Proof wiki: variance

psu.edu

newonlinecourses.science.psu.edu

"1.7.7 – Relationship between the Multinomial and Poisson | STAT 504". Archived from the original on 6 August 2019. Retrieved 6 August 2019.

rasch.org

Rasch, Georg (1963). The Poisson Process as a Model for a Diversity of Behavioural Phenomena (PDF). 17th International Congress of Psychology. Vol. 2. Washington, DC: American Psychological Association. doi:10.1037/e685262012-108.

rolandspeicher.com

Alexandru Nica, Roland Speicher: Lectures on the Combinatorics of Free Probability. London Mathematical Society Lecture Note Series, Vol. 335, Cambridge University Press, 2006.
Lectures on the Combinatorics of Free Probability by A. Nica and R. Speicher, pp. 203–204, Cambridge Univ. Press 2006

semanticscholar.org

api.semanticscholar.org

Helske, Jouni (2017). "KFAS: Exponential Family State Space Models in R". Journal of Statistical Software. 78 (10). arXiv:1612.01907. doi:10.18637/jss.v078.i10. S2CID 14379617.
Harremoes, P. (July 2001). "Binomial and Poisson distributions as maximum entropy distributions". IEEE Transactions on Information Theory. 47 (5): 2039–2041. doi:10.1109/18.930936. S2CID 16171405.
Kamath, Govinda M.; Şaşoğlu, Eren; Tse, David (14–19 June 2015). Optimal haplotype assembly from high-throughput mate-pair reads. 2015 IEEE International Symposium on Information Theory (ISIT). Hong Kong, China. pp. 914–918. arXiv:1502.01975. doi:10.1109/ISIT.2015.7282588. S2CID 128634.
Zhang, Huiming; Li, Bo (2016). "Characterizations of discrete compound Poisson distributions". Communications in Statistics - Theory and Methods. 45 (22): 6789–6802. doi:10.1080/03610926.2014.901375. S2CID 125475756.
Dytso, Alex; Poor, H. Vincent (2020). "Estimation in Poisson noise: Properties of the conditional mean estimator". IEEE Transactions on Information Theory. 66 (7): 4304–4323. arXiv:1911.03744. doi:10.1109/TIT.2020.2979978. S2CID 207853178.

sportsbettingonline.net

Hornby, Dave (2014). "Football Prediction Model: Poisson Distribution". Sports Betting Online. Retrieved 19 September 2014.

uni-stuttgart.de

digibus.ub.uni-stuttgart.de

von Bortkiewitsch, Ladislaus (1898). Das Gesetz der kleinen Zahlen [The law of small numbers] (in German). Leipzig, Germany: B.G. Teubner. pp. 1, 23–25.
On page 1, Bortkiewicz presents the Poisson distribution.

On pages 23–25, Bortkiewitsch presents his analysis of "4. Beispiel: Die durch Schlag eines Pferdes im preußischen Heere Getöteten." [4. Example: Those killed in the Prussian army by a horse's kick.]

web.archive.org

"1.7.7 – Relationship between the Multinomial and Poisson | STAT 504". Archived from the original on 6 August 2019. Retrieved 6 August 2019.
Breslow, Norman E.; Day, Nick E. (1987). Statistical Methods in Cancer Research. Vol. 2 — The Design and Analysis of Cohort Studies. Lyon, France: International Agency for Research on Cancer. ISBN 978-92-832-0182-3. Archived from the original on 8 August 2018. Retrieved 11 March 2012.

wolfram.com

reference.wolfram.com

"Wolfram Language: PoissonDistribution reference page". wolfram.com. Retrieved 8 April 2016.
"Wolfram Language: MultivariatePoissonDistribution reference page". wolfram.com. Retrieved 8 April 2016.

worldcat.org

Kardar, Mehran (2007). Statistical Physics of Particles. Cambridge University Press. p. 42. ISBN 978-0-521-87342-0. OCLC 860391091.
Mitzenmacher, Michael (2017). Probability and computing: Randomization and probabilistic techniques in algorithms and data analysis. Eli Upfal (2nd ed.). Cambridge, UK. Exercise 5.14. ISBN 978-1-107-15488-9. OCLC 960841613.{{cite book}}: CS1 maint: location missing publisher (link)
Van Trees, Harry L. (2013). Detection estimation and modulation theory. Kristine L. Bell, Zhi Tian (Second ed.). Hoboken, N.J. ISBN 978-1-299-66515-6. OCLC 851161356.{{cite book}}: CS1 maint: location missing publisher (link)
Lomnitz, Cinna (1994). Fundamentals of Earthquake Prediction. New York, NY: John Wiley & Sons. ISBN 0-471-57419-8. OCLC 647404423.
Katz, B.; Miledi, R. (August 1972). "The statistical nature of the acetylcholine potential and its molecular components". The Journal of Physiology. 224 (3): 665–699. doi:10.1113/jphysiol.1972.sp009918. ISSN 0022-3751. PMC 1331515. PMID 5071933.
Nelson, Philip Charles; Bromberg, Sarina; Hermundstad, Ann; Prentice, Jason (2015). Physical models of living systems. New York, NY: W.H. Freeman & Company, a Macmillan Education Imprint. ISBN 978-1-4641-4029-7. OCLC 891121698.

zenodo.org

a student (1907). "On the error of counting with a haemacytometer". Biometrika. 5 (3): 351–360. doi:10.2307/2331633. JSTOR 2331633.
Edgeworth, F.Y. (1913). "On the use of the theory of probabilities in statistics relating to society". Journal of the Royal Statistical Society. 76 (2): 165–193. doi:10.2307/2340091. JSTOR 2340091.