Normal distribution (English Wikipedia)

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

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Lyon, A. (2014). Why are Normal Distributions Normal?, The British Journal for the Philosophy of Science.

allisons.org

"Kullback Leibler (KL) Distance of Two Normal (Gaussian) Probability Distributions". Allisons.org. December 5, 2007. Retrieved March 3, 2017.

ams.org

mathscinet.ams.org

Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 26, eqn 26.2.12". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 932. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.
Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.

archive.org

"It has been customary certainly to regard as an axiom the hypothesis that if any quantity has been determined by several direct observations, made under the same circumstances and with equal care, the arithmetical mean of the observed values affords the most probable value, if not rigorously, yet very nearly at least, so that it is always most safe to adhere to it." — Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
McPherson (1990, p. 110) McPherson, Glen (1990). Statistics in Scientific Investigation: Its Basis, Application and Interpretation. Springer-Verlag. ISBN 978-0-387-97137-7.
Cover, Thomas M.; Thomas, Joy A. (2006). Elements of Information Theory. John Wiley and Sons. p. 254. ISBN 9780471748816.
Williams, David (2001). Weighing the odds : a course in probability and statistics (Reprinted. ed.). Cambridge [u.a.]: Cambridge Univ. Press. pp. 197–199. ISBN 978-0-521-00618-7.
Smith, José M. Bernardo; Adrian F. M. (2000). Bayesian theory (Reprint ed.). Chichester [u.a.]: Wiley. pp. 209, 366. ISBN 978-0-471-49464-5.{{cite book}}: CS1 maint: multiple names: authors list (link)
Galambos & Simonelli (2004, Theorem 3.5) Galambos, Janos; Simonelli, Italo (2004). Products of Random Variables: Applications to Problems of Physics and to Arithmetical Functions. Marcel Dekker, Inc. ISBN 978-0-8247-5402-0.
Stigler (1986, p. 76) Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press. ISBN 978-0-674-40340-6.
Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Gauss (1809, section 179) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Stigler (1986, p. 144) Stigler, Stephen M. (1986). The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press. ISBN 978-0-674-40340-6.

arxiv.org

Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. arXiv:1811.11301. doi:10.1007/s10479-019-03373-1. S2CID 254231768. Archived from the original (PDF) on March 31, 2023. Retrieved February 27, 2023.
Winkelbauer, Andreas (2012). "Moments and Absolute Moments of the Normal Distribution". arXiv:1209.4340 [math.ST].
Das, Abhranil (2021). "A method to integrate and classify normal distributions". Journal of Vision. 21 (10): 1. arXiv:2012.14331. doi:10.1167/jov.21.10.1. PMC 8419883. PMID 34468706.
Karney (2016) Karney, C. F. F. (2016). "Sampling exactly from the normal distribution". ACM Transactions on Mathematical Software. 42 (1): 3:1–14. arXiv:1303.6257. doi:10.1145/2710016. S2CID 14252035.

berkeley.edu

cs.berkeley.edu

Jordan, Michael I. (February 8, 2010). "Stat260: Bayesian Modeling and Inference: The Conjugate Prior for the Normal Distribution" (PDF).

bnf.fr

gallica.bnf.fr

Laplace (1774, Problem III) Laplace, Pierre-Simon de (1774). "Mémoire sur la probabilité des causes par les événements". Mémoires de l'Académie Royale des Sciences de Paris (Savants étrangers), Tome 6: 621–656. Translated by Stephen M. Stigler in Statistical Science 1 (3), 1986: JSTOR 2245476.

books.google.com

"It has been customary certainly to regard as an axiom the hypothesis that if any quantity has been determined by several direct observations, made under the same circumstances and with equal care, the arithmetical mean of the observed values affords the most probable value, if not rigorously, yet very nearly at least, so that it is always most safe to adhere to it." — Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Jaynes, Edwin T. (2003). Probability Theory: The Logic of Science. Cambridge University Press. pp. 592–593. ISBN 9780521592710.
Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Gauss (1809, section 179) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.
Gauss (1809, section 177) Gauss, Carolo Friderico (1809). Theoria motvs corporvm coelestivm in sectionibvs conicis Solem ambientivm [Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections] (in Latin). Hambvrgi, Svmtibvs F. Perthes et I. H. Besser. English translation.

cnx.org

Scott, Clayton; Nowak, Robert (August 7, 2003). "The Q-function". Connexions.

doi.org

"My custom of terming the curve the Gauss–Laplacian or normal curve saves us from proportioning the merit of discovery between the two great astronomer mathematicians." quote from Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.
Besides those specifically referenced here, such use is encountered in the works of Peirce, Galton (Galton (1889, chapter V)) and Lexis (Lexis (1878), Rohrbasser & Véron (2003)) c. 1875.^{[citation needed]} Galton, Francis (1889). Natural Inheritance (PDF). London, UK: Richard Clay and Sons. Lexis, Wilhelm (1878). "Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques". Annales de Démographie Internationale. II. Paris: 447–462. Rohrbasser, Jean-Marc; Véron, Jacques (2003). "Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things"". Population. 58 (3): 303–322. doi:10.3917/pope.303.0303.
Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. arXiv:1811.11301. doi:10.1007/s10479-019-03373-1. S2CID 254231768. Archived from the original (PDF) on March 31, 2023. Retrieved February 27, 2023.
Stigler (1982) Stigler, Stephen M. (1982). "A Modest Proposal: A New Standard for the Normal". The American Statistician. 36 (2): 137–138. doi:10.2307/2684031. JSTOR 2684031.
Halperin, Hartley & Hoel (1965, item 7) Halperin, Max; Hartley, Herman O.; Hoel, Paul G. (1965). "Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation". The American Statistician. 19 (3): 12–14. doi:10.2307/2681417. JSTOR 2681417.
Vaart, A. W. van der (October 13, 1998). Asymptotic Statistics. Cambridge University Press. doi:10.1017/cbo9780511802256. ISBN 978-0-511-80225-6.
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 March 7, 2016. Retrieved June 2, 2011.
Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.
Fan (1991, p. 1258) Fan, Jianqing (1991). "On the optimal rates of convergence for nonparametric deconvolution problems". The Annals of Statistics. 19 (3): 1257–1272. doi:10.1214/aos/1176348248. JSTOR 2241949.
Das, Abhranil (2021). "A method to integrate and classify normal distributions". Journal of Vision. 21 (10): 1. arXiv:2012.14331. doi:10.1167/jov.21.10.1. PMC 8419883. PMID 34468706.
Lukacs, Eugene (1942). "A Characterization of the Normal Distribution". The Annals of Mathematical Statistics. 13 (1): 91–3. doi:10.1214/aoms/1177731647. ISSN 0003-4851. JSTOR 2236166.
Lukacs & King (1954) Lukacs, Eugene; King, Edgar P. (1954). "A Property of Normal Distribution". The Annals of Mathematical Statistics. 25 (2): 389–394. doi:10.1214/aoms/1177728796. JSTOR 2236741.
John, S (1982). "The three parameter two-piece normal family of distributions and its fitting". Communications in Statistics – Theory and Methods. 11 (8): 879–885. doi:10.1080/03610928208828279.
Wichura, Michael J. (1988). "Algorithm AS241: The Percentage Points of the Normal Distribution". Applied Statistics. 37 (3): 477–84. doi:10.2307/2347330. JSTOR 2347330.
Kinderman & Monahan (1977) Kinderman, Albert J.; Monahan, John F. (1977). "Computer Generation of Random Variables Using the Ratio of Uniform Deviates". ACM Transactions on Mathematical Software. 3 (3): 257–260. doi:10.1145/355744.355750. S2CID 12884505.
Leva (1992) Leva, Joseph L. (1992). "A fast normal random number generator" (PDF). ACM Transactions on Mathematical Software. 18 (4): 449–453. CiteSeerX 10.1.1.544.5806. doi:10.1145/138351.138364. S2CID 15802663. Archived from the original (PDF) on July 16, 2010.
Marsaglia & Tsang (2000) Marsaglia, George; Tsang, Wai Wan (2000). "The Ziggurat Method for Generating Random Variables". Journal of Statistical Software. 5 (8). doi:10.18637/jss.v005.i08.
Karney (2016) Karney, C. F. F. (2016). "Sampling exactly from the normal distribution". ACM Transactions on Mathematical Software. 42 (1): 3:1–14. arXiv:1303.6257. doi:10.1145/2710016. S2CID 14252035.
Monahan (1985, section 2) Monahan, J. F. (1985). "Accuracy in random number generation". Mathematics of Computation. 45 (172): 559–568. doi:10.1090/S0025-5718-1985-0804945-X.
Wallace (1996) Wallace, C. S. (1996). "Fast pseudo-random generators for normal and exponential variates". ACM Transactions on Mathematical Software. 22 (1): 119–127. doi:10.1145/225545.225554. S2CID 18514848.
Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.
Stigler (1978, p. 243) Stigler, Stephen M. (1978). "Mathematical Statistics in the Early States". The Annals of Statistics. 6 (2): 239–265. doi:10.1214/aos/1176344123. JSTOR 2958876.
Stigler (1978, p. 244) Stigler, Stephen M. (1978). "Mathematical Statistics in the Early States". The Annals of Statistics. 6 (2): 239–265. doi:10.1214/aos/1176344123. JSTOR 2958876.
Maxwell (1860, p. 23) Maxwell, James Clerk (1860). "V. Illustrations of the dynamical theory of gases. — Part I: On the motions and collisions of perfectly elastic spheres". Philosophical Magazine. Series 4. 19 (124): 19–32. doi:10.1080/14786446008642818.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (June 22, 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme". Communications in Statistics – Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587.

dx.doi.org

Vaart, A. W. van der (October 13, 1998). Asymptotic Statistics. Cambridge University Press. doi:10.1017/cbo9780511802256. ISBN 978-0-511-80225-6.

encyclopedia.com

Normal Distribution, Gale Encyclopedia of Psychology

galton.org

Besides those specifically referenced here, such use is encountered in the works of Peirce, Galton (Galton (1889, chapter V)) and Lexis (Lexis (1878), Rohrbasser & Véron (2003)) c. 1875.^{[citation needed]} Galton, Francis (1889). Natural Inheritance (PDF). London, UK: Richard Clay and Sons. Lexis, Wilhelm (1878). "Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques". Annales de Démographie Internationale. II. Paris: 447–462. Rohrbasser, Jean-Marc; Véron, Jacques (2003). "Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things"". Population. 58 (3): 303–322. doi:10.3917/pope.303.0303.

inrialpes.fr

www-biba.inrialpes.fr

Jaynes, Edwin J.; Probability Theory: The Logic of Science, Ch. 7.

jstor.org

"My custom of terming the curve the Gauss–Laplacian or normal curve saves us from proportioning the merit of discovery between the two great astronomer mathematicians." quote from Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.
Stigler (1982) Stigler, Stephen M. (1982). "A Modest Proposal: A New Standard for the Normal". The American Statistician. 36 (2): 137–138. doi:10.2307/2684031. JSTOR 2684031.
Halperin, Hartley & Hoel (1965, item 7) Halperin, Max; Hartley, Herman O.; Hoel, Paul G. (1965). "Recommended Standards for Statistical Symbols and Notation. COPSS Committee on Symbols and Notation". The American Statistician. 19 (3): 12–14. doi:10.2307/2681417. JSTOR 2681417.
Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.
Fan (1991, p. 1258) Fan, Jianqing (1991). "On the optimal rates of convergence for nonparametric deconvolution problems". The Annals of Statistics. 19 (3): 1257–1272. doi:10.1214/aos/1176348248. JSTOR 2241949.
Lukacs, Eugene (1942). "A Characterization of the Normal Distribution". The Annals of Mathematical Statistics. 13 (1): 91–3. doi:10.1214/aoms/1177731647. ISSN 0003-4851. JSTOR 2236166.
Basu, D.; Laha, R. G. (1954). "On Some Characterizations of the Normal Distribution". Sankhyā. 13 (4): 359–62. ISSN 0036-4452. JSTOR 25048183.
Lukacs & King (1954) Lukacs, Eugene; King, Edgar P. (1954). "A Property of Normal Distribution". The Annals of Mathematical Statistics. 25 (2): 389–394. doi:10.1214/aoms/1177728796. JSTOR 2236741.
Wichura, Michael J. (1988). "Algorithm AS241: The Percentage Points of the Normal Distribution". Applied Statistics. 37 (3): 477–84. doi:10.2307/2347330. JSTOR 2347330.
Laplace (1774, Problem III) Laplace, Pierre-Simon de (1774). "Mémoire sur la probabilité des causes par les événements". Mémoires de l'Académie Royale des Sciences de Paris (Savants étrangers), Tome 6: 621–656. Translated by Stephen M. Stigler in Statistical Science 1 (3), 1986: JSTOR 2245476.
Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.
Stigler (1978, p. 243) Stigler, Stephen M. (1978). "Mathematical Statistics in the Early States". The Annals of Statistics. 6 (2): 239–265. doi:10.1214/aos/1176344123. JSTOR 2958876.
Stigler (1978, p. 244) Stigler, Stephen M. (1978). "Mathematical Statistics in the Early States". The Annals of Statistics. 6 (2): 239–265. doi:10.1214/aos/1176344123. JSTOR 2958876.

loc.gov

lccn.loc.gov

Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 26, eqn 26.2.12". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 932. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

loc.gov

Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 26, eqn 26.2.12". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 932. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

mathsisfun.com

"Normal Distribution". www.mathsisfun.com. Retrieved August 15, 2020.

nih.gov

ncbi.nlm.nih.gov

Das, Abhranil (2021). "A method to integrate and classify normal distributions". Journal of Vision. 21 (10): 1. arXiv:2012.14331. doi:10.1167/jov.21.10.1. PMC 8419883. PMID 34468706.

pubmed.ncbi.nlm.nih.gov

Das, Abhranil (2021). "A method to integrate and classify normal distributions". Journal of Vision. 21 (10): 1. arXiv:2012.14331. doi:10.1167/jov.21.10.1. PMC 8419883. PMID 34468706.

persee.fr

Besides those specifically referenced here, such use is encountered in the works of Peirce, Galton (Galton (1889, chapter V)) and Lexis (Lexis (1878), Rohrbasser & Véron (2003)) c. 1875.^{[citation needed]} Galton, Francis (1889). Natural Inheritance (PDF). London, UK: Richard Clay and Sons. Lexis, Wilhelm (1878). "Sur la durée normale de la vie humaine et sur la théorie de la stabilité des rapports statistiques". Annales de Démographie Internationale. II. Paris: 447–462. Rohrbasser, Jean-Marc; Véron, Jacques (2003). "Wilhelm Lexis: The Normal Length of Life as an Expression of the "Nature of Things"". Population. 58 (3): 303–322. doi:10.3917/pope.303.0303.

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 March 7, 2016. Retrieved June 2, 2011.
Leva (1992) Leva, Joseph L. (1992). "A fast normal random number generator" (PDF). ACM Transactions on Mathematical Software. 18 (4): 449–453. CiteSeerX 10.1.1.544.5806. doi:10.1145/138351.138364. S2CID 15802663. Archived from the original (PDF) on July 16, 2010.

semanticscholar.org

api.semanticscholar.org

Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. arXiv:1811.11301. doi:10.1007/s10479-019-03373-1. S2CID 254231768. Archived from the original (PDF) on March 31, 2023. Retrieved February 27, 2023.
Kinderman & Monahan (1977) Kinderman, Albert J.; Monahan, John F. (1977). "Computer Generation of Random Variables Using the Ratio of Uniform Deviates". ACM Transactions on Mathematical Software. 3 (3): 257–260. doi:10.1145/355744.355750. S2CID 12884505.
Leva (1992) Leva, Joseph L. (1992). "A fast normal random number generator" (PDF). ACM Transactions on Mathematical Software. 18 (4): 449–453. CiteSeerX 10.1.1.544.5806. doi:10.1145/138351.138364. S2CID 15802663. Archived from the original (PDF) on July 16, 2010.
Karney (2016) Karney, C. F. F. (2016). "Sampling exactly from the normal distribution". ACM Transactions on Mathematical Software. 42 (1): 3:1–14. arXiv:1303.6257. doi:10.1145/2710016. S2CID 14252035.
Wallace (1996) Wallace, C. S. (1996). "Fast pseudo-random generators for normal and exponential variates". ACM Transactions on Mathematical Software. 22 (1): 119–127. doi:10.1145/225545.225554. S2CID 18514848.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (June 22, 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme". Communications in Statistics – Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587.

stackexchange.com

math.stackexchange.com

"Expectation of the maximum of gaussian random variables". Mathematics Stack Exchange. Retrieved April 7, 2024.

stonybrook.edu

uryasev.ams.stonybrook.edu

Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. arXiv:1811.11301. doi:10.1007/s10479-019-03373-1. S2CID 254231768. Archived from the original (PDF) on March 31, 2023. Retrieved February 27, 2023.

tandfonline.com

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

tau.ac.il

eng.tau.ac.il

Barak, Ohad (April 6, 2006). "Q Function and Error Function" (PDF). Tel Aviv University. Archived from the original (PDF) on March 25, 2009.

tripod.com

jeff560.tripod.com

"Earliest Uses... (Entry Standard Normal Curve)".

ubc.ca

math.ubc.ca

Abramowitz, Milton; Stegun, Irene Ann, eds. (1983) [June 1964]. "Chapter 26, eqn 26.2.12". Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series. Vol. 55 (Ninth reprint with additional corrections of tenth original printing with corrections (December 1972); first ed.). Washington D.C.; New York: United States Department of Commerce, National Bureau of Standards; Dover Publications. p. 932. ISBN 978-0-486-61272-0. LCCN 64-60036. MR 0167642. LCCN 65-12253.

ucla.edu

stat.ucla.edu

"Normal Approximation to Poisson Distribution". Stat.ucla.edu. Retrieved March 3, 2017.

uconn.edu

saluc.engr.uconn.edu

Leva (1992) Leva, Joseph L. (1992). "A fast normal random number generator" (PDF). ACM Transactions on Mathematical Software. 18 (4): 449–453. CiteSeerX 10.1.1.544.5806. doi:10.1145/138351.138364. S2CID 15802663. Archived from the original (PDF) on July 16, 2010.

uiuc.edu

math.uiuc.edu

UIUC, Lecture 21. The Multivariate Normal Distribution, 21.6:"Individually Gaussian Versus Jointly Gaussian".

uni.wroc.pl

math.uni.wroc.pl

Quine, M.P. (1993). "On three characterisations of the normal distribution". Probability and Mathematical Statistics. 14 (2): 257–263.

waterlog.info

Oosterbaan, Roland J. (1994). "Chapter 6: Frequency and Regression Analysis of Hydrologic Data" (PDF). In Ritzema, Henk P. (ed.). Drainage Principles and Applications, Publication 16 (second revised ed.). Wageningen, The Netherlands: International Institute for Land Reclamation and Improvement (ILRI). pp. 175–224. ISBN 978-90-70754-33-4.

web.archive.org

Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. arXiv:1811.11301. doi:10.1007/s10479-019-03373-1. S2CID 254231768. Archived from the original (PDF) on March 31, 2023. Retrieved February 27, 2023.
Barak, Ohad (April 6, 2006). "Q Function and Error Function" (PDF). Tel Aviv University. Archived from the original (PDF) on March 25, 2009.
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 March 7, 2016. Retrieved June 2, 2011.
Leva (1992) Leva, Joseph L. (1992). "A fast normal random number generator" (PDF). ACM Transactions on Mathematical Software. 18 (4): 449–453. CiteSeerX 10.1.1.544.5806. doi:10.1145/138351.138364. S2CID 15802663. Archived from the original (PDF) on July 16, 2010.

wikidata.org

Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Normal Distribution Function". MathWorld.
Weisstein, Eric W. "Normal Product Distribution". MathWorld. wolfram.com.

worldcat.org

search.worldcat.org

Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.
Lukacs, Eugene (1942). "A Characterization of the Normal Distribution". The Annals of Mathematical Statistics. 13 (1): 91–3. doi:10.1214/aoms/1177731647. ISSN 0003-4851. JSTOR 2236166.
Basu, D.; Laha, R. G. (1954). "On Some Characterizations of the Normal Distribution". Sankhyā. 13 (4): 359–62. ISSN 0036-4452. JSTOR 25048183.
Huxley (1932) Huxley, Julian S. (1932). Problems of Relative Growth. London. ISBN 978-0-486-61114-3. OCLC 476909537.
Sun, Jingchao; Kong, Maiying; Pal, Subhadip (June 22, 2021). "The Modified-Half-Normal distribution: Properties and an efficient sampling scheme". Communications in Statistics – Theory and Methods. 52 (5): 1591–1613. doi:10.1080/03610926.2021.1934700. ISSN 0361-0926. S2CID 237919587.

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 March 7, 2016. Retrieved June 2, 2011.

yale.edu

stat.yale.edu

"The Normal Distribution". Statistical Topics: definitions, explanations, and examples for each of the major concepts covered in Statistics 101-103. Yale University. Retrieved November 17, 2024.

york.ac.uk

De Moivre, Abraham (1733), Corollary I – see Walker (1985, p. 77) Walker, Helen M. (1985). "De Moivre on the Law of Normal Probability" (PDF). In Smith, David Eugene (ed.). A Source Book in Mathematics. Dover. ISBN 978-0-486-64690-9.

zbmath.org

Lukacs, Eugene (March 1942). "A Characterization of the Normal Distribution". Annals of Mathematical Statistics. 13 (1): 91–93. doi:10.1214/AOMS/1177731647. ISSN 0003-4851. JSTOR 2236166. MR 0006626. Zbl 0060.28509. Wikidata Q55897617.

zenodo.org

"My custom of terming the curve the Gauss–Laplacian or normal curve saves us from proportioning the merit of discovery between the two great astronomer mathematicians." quote from Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.
Pearson (1905, p. 189) Pearson, Karl (1905). "'Das Fehlergesetz und seine Verallgemeinerungen durch Fechner und Pearson'. A rejoinder". Biometrika. 4 (1): 169–212. doi:10.2307/2331536. JSTOR 2331536.