Central limit theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Central limit theorem" in English language version.

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Fischer (2011), p. ^{[page needed]}. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
Stein, C. (1972). "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables". Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. 6 (2): 583–602. MR 0402873. Zbl 0278.60026.
Fischer (2011), Chapter 2; Chapter 5.2. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.

arxiv.org

Klartag (2007), Theorem 1.2. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Klartag (2008), Theorem 1. Klartag, Bo'az (2008). "A Berry–Esseen type inequality for convex bodies with an unconditional basis". Probability Theory and Related Fields. 145 (1–2): 1–33. arXiv:0705.0832. doi:10.1007/s00440-008-0158-6. S2CID 10163322.
Klartag (2007), Theorem 1.1. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Bárány & Vu (2007), Theorem 1.1. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Bárány & Vu (2007), Theorem 1.2. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Meckes, Elizabeth (2008). "Linear functions on the classical matrix groups". Transactions of the American Mathematical Society. 360 (10): 5355–5366. arXiv:math/0509441. doi:10.1090/S0002-9947-08-04444-9. S2CID 11981408.

books.google.com

Petrov, V. V. (1976). Sums of Independent Random Variables. New York-Heidelberg: Springer-Verlag. ch. 7. ISBN 9783642658099.

cmu.edu

contrib.andrew.cmu.edu

O’Donnell, Ryan (2014). "Theorem 5.38". Archived from the original on 2019-04-08. Retrieved 2017-10-18.

doi.org

Fischer (2011), p. ^{[page needed]}. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
Robbins, Herbert (1948). "The asymptotic distribution of the sum of a random number of random variables". Bull. Amer. Math. Soc. 54 (12): 1151–1161. doi:10.1090/S0002-9904-1948-09142-X.
Bentkus, V. (2005). "A Lyapunov-type bound in $\mathbb {R} ^{d}$ ". Theory Probab. Appl. 49 (2): 311–323. doi:10.1137/S0040585X97981123.
Nolan, John P. (2020). Univariate stable distributions, Models for Heavy Tailed Data. Springer Series in Operations Research and Financial Engineering. Switzerland: Springer. doi:10.1007/978-3-030-52915-4. ISBN 978-3-030-52914-7. S2CID 226648987.
Lemons, Don (2003). An Introduction to Stochastic Processes in Physics. Johns Hopkins University Press. doi:10.56021/9780801868665. ISBN 9780801876387. Retrieved 2016-08-11.
Artstein, S.; Ball, K.; Barthe, F.; Naor, A. (2004). "Solution of Shannon's Problem on the Monotonicity of Entropy". Journal of the American Mathematical Society. 17 (4): 975–982. doi:10.1090/S0894-0347-04-00459-X.
Brewer, J. K. (1985). "Behavioral statistics textbooks: Source of myths and misconceptions?". Journal of Educational Statistics. 10 (3): 252–268. doi:10.3102/10769986010003252. S2CID 119611584.
Sotos, A. E. C.; Vanhoof, S.; Van den Noortgate, W.; Onghena, P. (2007). "Students' misconceptions of statistical inference: A review of the empirical evidence from research on statistics education". Educational Research Review. 2 (2): 98–113. doi:10.1016/j.edurev.2007.04.001.
Hew, Patrick Chisan (2017). "Asymptotic distribution of rewards accumulated by alternating renewal processes". Statistics and Probability Letters. 129: 355–359. doi:10.1016/j.spl.2017.06.027.
Rempala, G.; Wesolowski, J. (2002). "Asymptotics of products of sums and U-statistics" (PDF). Electronic Communications in Probability. 7: 47–54. doi:10.1214/ecp.v7-1046.
Klartag (2007), Theorem 1.2. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Klartag (2008), Theorem 1. Klartag, Bo'az (2008). "A Berry–Esseen type inequality for convex bodies with an unconditional basis". Probability Theory and Related Fields. 145 (1–2): 1–33. arXiv:0705.0832. doi:10.1007/s00440-008-0158-6. S2CID 10163322.
Klartag (2007), Theorem 1.1. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Gaposhkin (1966), Theorem 2.1.13. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..
Bárány & Vu (2007), Theorem 1.1. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Bárány & Vu (2007), Theorem 1.2. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Meckes, Elizabeth (2008). "Linear functions on the classical matrix groups". Transactions of the American Mathematical Society. 360 (10): 5355–5366. arXiv:math/0509441. doi:10.1090/S0002-9947-08-04444-9. S2CID 11981408.
Gaposhkin (1966), Sect. 1.5. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..
Pólya, George (1920). "Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem" [On the central limit theorem of probability calculation and the problem of moments]. Mathematische Zeitschrift (in German). 8 (3–4): 171–181. doi:10.1007/BF01206525. S2CID 123063388.
Le Cam, Lucien (1986). "The central limit theorem around 1935". Statistical Science. 1 (1): 78–91. doi:10.1214/ss/1177013818.
Fischer (2011), Chapter 2; Chapter 5.2. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
Zabell, S. L. (1995). "Alan Turing and the Central Limit Theorem". American Mathematical Monthly. 102 (6): 483–494. doi:10.1080/00029890.1995.12004608.

galton.org

Galton, F. (1889). Natural Inheritance. p. 66.

gbv.de

Hald, Andreas (22 April 1998). A History of Mathematical Statistics from 1750 to 1930 (PDF). Wiley. chapter 17. ISBN 978-0471179122. Archived (PDF) from the original on 2022-10-09.

ghostarchive.org

Rouaud, Mathieu (2013). Probability, Statistics and Estimation (PDF). p. 10. Archived (PDF) from the original on 2022-10-09.
Hald, Andreas (22 April 1998). A History of Mathematical Statistics from 1750 to 1930 (PDF). Wiley. chapter 17. ISBN 978-0471179122. Archived (PDF) from the original on 2022-10-09.

harvard.edu

ui.adsabs.harvard.edu

Klartag (2007), Theorem 1.2. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Klartag (2007), Theorem 1.1. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Gaposhkin (1966), Theorem 2.1.13. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..
Gaposhkin (1966), Sect. 1.5. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..

incertitudes.fr

Rouaud, Mathieu (2013). Probability, Statistics and Estimation (PDF). p. 10. Archived (PDF) from the original on 2022-10-09.

jhu.edu

jhupbooks.press.jhu.edu

Lemons, Don (2003). An Introduction to Stochastic Processes in Physics. Johns Hopkins University Press. doi:10.56021/9780801868665. ISBN 9780801876387. Retrieved 2016-08-11.

jstor.org

Le Cam, L. (February 1986). "The Central Limit Theorem around 1935". Statistical Science. 1 (1): 78–91. JSTOR 2245503.

khanacademy.org

"Sampling distribution of the sample mean". Khan Academy. 2 June 2023. Archived from the original (video) on 2023-06-02. Retrieved 2023-10-08.

kuleuven.be

lirias.kuleuven.be

Sotos, A. E. C.; Vanhoof, S.; Van den Noortgate, W.; Onghena, P. (2007). "Students' misconceptions of statistical inference: A review of the empirical evidence from research on statistics education". Educational Research Review. 2 (2): 98–113. doi:10.1016/j.edurev.2007.04.001.

loc.gov

lccn.loc.gov

van der Vaart, A.W. (1998). Asymptotic statistics. New York, NY: Cambridge University Press. ISBN 978-0-521-49603-2. LCCN 98015176.

mcgill.ca

medicine.mcgill.ca

Fischer (2011), p. ^{[page needed]}. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
Fischer (2011), Chapter 2; Chapter 5.2. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.

projecteuclid.org

Robbins, Herbert (1948). "The asymptotic distribution of the sum of a random number of random variables". Bull. Amer. Math. Soc. 54 (12): 1151–1161. doi:10.1090/S0002-9904-1948-09142-X.
Stein, C. (1972). "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables". Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. 6 (2): 583–602. MR 0402873. Zbl 0278.60026.
Rempala, G.; Wesolowski, J. (2002). "Asymptotics of products of sums and U-statistics" (PDF). Electronic Communications in Probability. 7: 47–54. doi:10.1214/ecp.v7-1046.
Le Cam, Lucien (1986). "The central limit theorem around 1935". Statistical Science. 1 (1): 78–91. doi:10.1214/ss/1177013818.

semanticscholar.org

api.semanticscholar.org

Nolan, John P. (2020). Univariate stable distributions, Models for Heavy Tailed Data. Springer Series in Operations Research and Financial Engineering. Switzerland: Springer. doi:10.1007/978-3-030-52915-4. ISBN 978-3-030-52914-7. S2CID 226648987.
Brewer, J. K. (1985). "Behavioral statistics textbooks: Source of myths and misconceptions?". Journal of Educational Statistics. 10 (3): 252–268. doi:10.3102/10769986010003252. S2CID 119611584.
Klartag (2007), Theorem 1.2. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Klartag (2008), Theorem 1. Klartag, Bo'az (2008). "A Berry–Esseen type inequality for convex bodies with an unconditional basis". Probability Theory and Related Fields. 145 (1–2): 1–33. arXiv:0705.0832. doi:10.1007/s00440-008-0158-6. S2CID 10163322.
Klartag (2007), Theorem 1.1. Klartag, Bo'az (2007). "A central limit theorem for convex sets". Inventiones Mathematicae. 168 (1): 91–131. arXiv:math/0605014. Bibcode:2007InMat.168...91K. doi:10.1007/s00222-006-0028-8. S2CID 119169773.
Gaposhkin (1966), Theorem 2.1.13. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..
Bárány & Vu (2007), Theorem 1.1. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Bárány & Vu (2007), Theorem 1.2. Bárány, Imre; Vu, Van (2007). "Central limit theorems for Gaussian polytopes". Annals of Probability. 35 (4). Institute of Mathematical Statistics: 1593–1621. arXiv:math/0610192. doi:10.1214/009117906000000791. S2CID 9128253.
Meckes, Elizabeth (2008). "Linear functions on the classical matrix groups". Transactions of the American Mathematical Society. 360 (10): 5355–5366. arXiv:math/0509441. doi:10.1090/S0002-9947-08-04444-9. S2CID 11981408.
Gaposhkin (1966), Sect. 1.5. Gaposhkin, V. F. (1966). "Lacunary series and independent functions". Russian Mathematical Surveys. 21 (6): 1–82. Bibcode:1966RuMaS..21....1G. doi:10.1070/RM1966v021n06ABEH001196. S2CID 250833638..
Pólya, George (1920). "Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem" [On the central limit theorem of probability calculation and the problem of moments]. Mathematische Zeitschrift (in German). 8 (3–4): 171–181. doi:10.1007/BF01206525. S2CID 123063388.

uni-goettingen.de

www-gdz.sub.uni-goettingen.de

Pólya, George (1920). "Über den zentralen Grenzwertsatz der Wahrscheinlichkeitsrechnung und das Momentenproblem" [On the central limit theorem of probability calculation and the problem of moments]. Mathematische Zeitschrift (in German). 8 (3–4): 171–181. doi:10.1007/BF01206525. S2CID 123063388.

web.archive.org

Fischer (2011), p. ^{[page needed]}. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
O’Donnell, Ryan (2014). "Theorem 5.38". Archived from the original on 2019-04-08. Retrieved 2017-10-18.
"Sampling distribution of the sample mean". Khan Academy. 2 June 2023. Archived from the original (video) on 2023-06-02. Retrieved 2023-10-08.
Fischer (2011), Chapter 2; Chapter 5.2. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.

zbmath.org

Fischer (2011), p. ^{[page needed]}. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.
Stein, C. (1972). "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables". Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. 6 (2): 583–602. MR 0402873. Zbl 0278.60026.
Fischer (2011), Chapter 2; Chapter 5.2. Fischer, Hans (2011). A History of the Central Limit Theorem: From Classical to Modern Probability Theory (PDF). Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer. doi:10.1007/978-0-387-87857-7. ISBN 978-0-387-87856-0. MR 2743162. Zbl 1226.60004. Archived (PDF) from the original on 2017-10-31.