Chebyshev's inequality (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Chebyshev's inequality" in English language version.

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26doi.org

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Birnbaum, Z. W.; Raymond, J.; Zuckerman, H. S. (1947). "A Generalization of Tshebyshev's Inequality to Two Dimensions". The Annals of Mathematical Statistics. 18 (1): 70–79. doi:10.1214/aoms/1177730493. ISSN 0003-4851. MR 0019849. Zbl 0032.03402. Retrieved 7 October 2012.
Olkin, Ingram; Pratt, John W. (1958). "A Multivariate Tchebycheff Inequality". The Annals of Mathematical Statistics. 29 (1): 226–234. doi:10.1214/aoms/1177706720. MR 0093865. Zbl 0085.35204.
Fink, A. M.; Jodeit, Max Jr. (1984). "On Chebyshev's other inequality". In Tong, Y. L.; Gupta, Shanti S. (eds.). Inequalities in Statistics and Probability. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Vol. 5. pp. 115–120. doi:10.1214/lnms/1215465637. ISBN 978-0-940600-04-1. MR 0789242. Retrieved 7 October 2012.
Malamud, S. M. (15 February 2001). "Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter". Proceedings of the American Mathematical Society. 129 (9): 2671–2678. doi:10.1090/S0002-9939-01-05849-X. ISSN 0002-9939. MR 1838791. Retrieved 7 October 2012.

ams.org

Malamud, S. M. (15 February 2001). "Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter". Proceedings of the American Mathematical Society. 129 (9): 2671–2678. doi:10.1090/S0002-9939-01-05849-X. ISSN 0002-9939. MR 1838791. Retrieved 7 October 2012.

arxiv.org (Global: 69^th place; English: 59^th place)

Xinjia Chen (2007). "A New Generalization of Chebyshev Inequality for Random Vectors". arXiv:0707.0805v2 [math.ST].
Stellato, Bartolomeo; Parys, Bart P. G. Van; Goulart, Paul J. (2016-05-31). "Multivariate Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 71 (2): 123–127. arXiv:1509.08398. doi:10.1080/00031305.2016.1186559. ISSN 0003-1305. S2CID 53407286.

books.google.com (Global: 3^rd place; English: 3^rd place)

Kvanli, Alan H.; Pavur, Robert J.; Keeling, Kellie B. (2006). Concise Managerial Statistics. cEngage Learning. pp. 81–82. ISBN 978-0-324-22388-0.
Chernick, Michael R. (2011). The Essentials of Biostatistics for Physicians, Nurses, and Clinicians. John Wiley & Sons. pp. 49–50. ISBN 978-0-470-64185-9.

britannica.com (Global: 40^th place; English: 58^th place)

Routledge, Richard. Chebyshev's inequality. Encyclopedia Britannica.

cambridge.org (Global: 305^th place; English: 264^th place)

Mitzenmacher, Michael; Upfal, Eli (January 2005). Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Repr. ed.). Cambridge [u.a.]: Cambridge Univ. Press. ISBN 978-0-521-83540-4. Retrieved 6 October 2012.

cirano.qc.ca (Global: low place; English: low place)

www2.cirano.qc.ca

Dufour (2003) Properties of moments of random variables

csm.ro (Global: low place; English: low place)

Niculescu, Constantin P.; Pečarić, Josip (2010). "The Equivalence of Chebyshev's Inequality to the Hermite–Hadamard Inequality" (PDF). Mathematical Reports. 12 (62): 145–156. ISSN 1582-3067. Retrieved 6 October 2012.

demon.co.uk (Global: 3,292^nd place; English: 2,192^nd place)

mcdowella.demon.co.uk

Grimmett and Stirzaker, problem 7.11.9. Several proofs of this result can be found in Chebyshev's Inequalities Archived 2019-02-24 at the Wayback Machine by A. G. McDowell.

doi.org (Global: 2^nd place; English: 2^nd place)

Uhl, Roland (2023). Charakterisierung des Erwartungswertes am Graphen der Verteilungsfunktion [Characterization of the expected value on the graph of the cumulative distribution function] (PDF). Technische Hochschule Brandenburg. p. 5. doi:10.25933/opus4-2986. Archived from the original on 2023-12-24.
Selberg, Henrik L. (1940). "Zwei Ungleichungen zur Ergänzung des Tchebycheffschen Lemmas" [Two Inequalities Supplementing the Tchebycheff Lemma]. Skandinavisk Aktuarietidskrift (Scandinavian Actuarial Journal) (in German). 1940 (3–4): 121–125. doi:10.1080/03461238.1940.10404804. ISSN 0346-1238. OCLC 610399869.
Godwin, H. J. (September 1955). "On Generalizations of Tchebychef's Inequality". Journal of the American Statistical Association. 50 (271): 923–945. doi:10.1080/01621459.1955.10501978. ISSN 0162-1459.
Birnbaum, Z. W.; Raymond, J.; Zuckerman, H. S. (1947). "A Generalization of Tshebyshev's Inequality to Two Dimensions". The Annals of Mathematical Statistics. 18 (1): 70–79. doi:10.1214/aoms/1177730493. ISSN 0003-4851. MR 0019849. Zbl 0032.03402. Retrieved 7 October 2012.
Ferentinos, K (1982). "On Tchebycheff type inequalities". Trabajos Estadıst Investigacion Oper. 33: 125–132. doi:10.1007/BF02888707. S2CID 123762564.
Jorge Navarro (2014). "Can the bounds in the multivariate Chebyshev inequality be attained?". Statistics and Probability Letters. 91: 1–5. doi:10.1016/j.spl.2014.03.028.
Stellato, Bartolomeo; Parys, Bart P. G. Van; Goulart, Paul J. (2016-05-31). "Multivariate Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 71 (2): 123–127. arXiv:1509.08398. doi:10.1080/00031305.2016.1186559. ISSN 0003-1305. S2CID 53407286.
Vandenberghe, L.; Boyd, S.; Comanor, K. (2007-01-01). "Generalized Chebyshev Bounds via Semidefinite Programming". SIAM Review. 49 (1): 52–64. Bibcode:2007SIAMR..49...52V. CiteSeerX 10.1.1.126.9105. doi:10.1137/S0036144504440543. ISSN 0036-1445.
Berge, P. O. (1938). "A note on a form of Tchebycheff's theorem for two variables". Biometrika. 29 (3/4): 405–406. doi:10.2307/2332015. JSTOR 2332015.
Olkin, Ingram; Pratt, John W. (1958). "A Multivariate Tchebycheff Inequality". The Annals of Mathematical Statistics. 29 (1): 226–234. doi:10.1214/aoms/1177706720. MR 0093865. Zbl 0085.35204.
Baranoski, Gladimir V. G.; Rokne, Jon G.; Xu, Guangwu (15 May 2001). "Applying the exponential Chebyshev inequality to the nondeterministic computation of form factors". Journal of Quantitative Spectroscopy and Radiative Transfer. 69 (4): 199–200. Bibcode:2001JQSRT..69..447B. doi:10.1016/S0022-4073(00)00095-9. (the references for this article are corrected by Baranoski, Gladimir V. G.; Rokne, Jon G.; Guangwu Xu (15 January 2002). "Corrigendum to: 'Applying the exponential Chebyshev inequality to the nondeterministic computation of form factors'". Journal of Quantitative Spectroscopy and Radiative Transfer. 72 (2): 199–200. Bibcode:2002JQSRT..72..199B. doi:10.1016/S0022-4073(01)00171-6.)
Saw, John G.; Yang, Mark C. K.; Mo, Tse Chin (1984). "Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 38 (2): 130–2. doi:10.2307/2683249. ISSN 0003-1305. JSTOR 2683249.
Kabán, Ata (2012). "Non-parametric detection of meaningless distances in high dimensional data". Statistics and Computing. 22 (2): 375–85. doi:10.1007/s11222-011-9229-0. S2CID 6018114.
Konijn, Hendrik S. (February 1987). "Distribution-Free and Other Prediction Intervals". The American Statistician. 41 (1): 11–15. doi:10.2307/2684311. JSTOR 2684311.
Beasley, T. Mark; Page, Grier P.; Brand, Jaap P. L.; Gadbury, Gary L.; Mountz, John D.; Allison, David B. (January 2004). "Chebyshev's inequality for nonparametric testing with small N and α in microarray research". Journal of the Royal Statistical Society. C (Applied Statistics). 53 (1): 95–108. doi:10.1111/j.1467-9876.2004.00428.x. ISSN 1467-9876. S2CID 122678278.
Berck, Peter; Hihn, Jairus M. (May 1982). "Using the Semivariance to Estimate Safety-First Rules". American Journal of Agricultural Economics. 64 (2): 298–300. doi:10.2307/1241139. ISSN 0002-9092. JSTOR 1241139.
Nantell, Timothy J.; Price, Barbara (June 1979). "An Analytical Comparison of Variance and Semivariance Capital Market Theories". The Journal of Financial and Quantitative Analysis. 14 (2): 221–42. doi:10.2307/2330500. JSTOR 2330500. S2CID 154652959.
Neave, Edwin H.; Ross, Michael N.; Yang, Jun (2009). "Distinguishing upside potential from downside risk". Management Research News. 32 (1): 26–36. doi:10.1108/01409170910922005. ISSN 0140-9174.
Bhattacharyya, B. B. (1987). "One-sided chebyshev inequality when the first four moments are known". Communications in Statistics – Theory and Methods. 16 (9): 2789–91. doi:10.1080/03610928708829540. ISSN 0361-0926.
Pukelsheim, Friedrich (May 1994). "The Three Sigma Rule". The American Statistician. 48 (2): 88–91. doi:10.1080/00031305.1994.10476030. ISSN 0003-1305. S2CID 122587510.
DasGupta, A (2000). "Best constants in Chebychev inequalities with various applications". Metrika. 5 (1): 185–200. doi:10.1007/s184-000-8316-9. S2CID 121436601.
Haldane, J. B. (1952). "Simple tests for bimodality and bitangentiality". Annals of Eugenics. 16 (4): 359–364. doi:10.1111/j.1469-1809.1951.tb02488.x. PMID 14953132.
He, Simai; Zhang, Jiawei; Zhang, Shuzhong (2010). "Bounding probability of small deviation: a fourth moment approach". Mathematics of Operations Research. 35 (1): 208–232. doi:10.1287/moor.1090.0438. S2CID 11298475.
Fink, A. M.; Jodeit, Max Jr. (1984). "On Chebyshev's other inequality". In Tong, Y. L.; Gupta, Shanti S. (eds.). Inequalities in Statistics and Probability. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Vol. 5. pp. 115–120. doi:10.1214/lnms/1215465637. ISBN 978-0-940600-04-1. MR 0789242. Retrieved 7 October 2012.
Niculescu, Constantin P. (2001). "An extension of Chebyshev's inequality and its connection with Jensen's inequality". Journal of Inequalities and Applications. 6 (4): 451–462. CiteSeerX 10.1.1.612.7056. doi:10.1155/S1025583401000273. ISSN 1025-5834. Retrieved 6 October 2012.
Malamud, S. M. (15 February 2001). "Some complements to the Jensen and Chebyshev inequalities and a problem of W. Walter". Proceedings of the American Mathematical Society. 129 (9): 2671–2678. doi:10.1090/S0002-9939-01-05849-X. ISSN 0002-9939. MR 1838791. Retrieved 7 October 2012.

epa.gov (Global: 882^nd place; English: 600^th place)

nepis.epa.gov

Calculating Upper Confidence Limits for Exposure Point Concentrations at hazardous Waste Sites (Report). Office of Emergency and Remedial Response of the U.S. Environmental Protection Agency. December 2002. Retrieved 5 August 2016.

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Vandenberghe, L.; Boyd, S.; Comanor, K. (2007-01-01). "Generalized Chebyshev Bounds via Semidefinite Programming". SIAM Review. 49 (1): 52–64. Bibcode:2007SIAMR..49...52V. CiteSeerX 10.1.1.126.9105. doi:10.1137/S0036144504440543. ISSN 0036-1445.
Baranoski, Gladimir V. G.; Rokne, Jon G.; Xu, Guangwu (15 May 2001). "Applying the exponential Chebyshev inequality to the nondeterministic computation of form factors". Journal of Quantitative Spectroscopy and Radiative Transfer. 69 (4): 199–200. Bibcode:2001JQSRT..69..447B. doi:10.1016/S0022-4073(00)00095-9. (the references for this article are corrected by Baranoski, Gladimir V. G.; Rokne, Jon G.; Guangwu Xu (15 January 2002). "Corrigendum to: 'Applying the exponential Chebyshev inequality to the nondeterministic computation of form factors'". Journal of Quantitative Spectroscopy and Radiative Transfer. 72 (2): 199–200. Bibcode:2002JQSRT..72..199B. doi:10.1016/S0022-4073(01)00171-6.)

ijpam.eu (Global: low place; English: low place)

Steliga, Katarzyna; Szynal, Dominik (2010). "On Markov-Type Inequalities" (PDF). International Journal of Pure and Applied Mathematics. 58 (2): 137–152. ISSN 1311-8080. Retrieved 10 October 2012.

jstor.org (Global: 26^th place; English: 20^th place)

Berge, P. O. (1938). "A note on a form of Tchebycheff's theorem for two variables". Biometrika. 29 (3/4): 405–406. doi:10.2307/2332015. JSTOR 2332015.
Saw, John G.; Yang, Mark C. K.; Mo, Tse Chin (1984). "Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 38 (2): 130–2. doi:10.2307/2683249. ISSN 0003-1305. JSTOR 2683249.
Konijn, Hendrik S. (February 1987). "Distribution-Free and Other Prediction Intervals". The American Statistician. 41 (1): 11–15. doi:10.2307/2684311. JSTOR 2684311.
Berck, Peter; Hihn, Jairus M. (May 1982). "Using the Semivariance to Estimate Safety-First Rules". American Journal of Agricultural Economics. 64 (2): 298–300. doi:10.2307/1241139. ISSN 0002-9092. JSTOR 1241139.
Nantell, Timothy J.; Price, Barbara (June 1979). "An Analytical Comparison of Variance and Semivariance Capital Market Theories". The Journal of Financial and Quantitative Analysis. 14 (2): 221–42. doi:10.2307/2330500. JSTOR 2330500. S2CID 154652959.

kobv.de (Global: low place; English: low place)

opus4.kobv.de

Uhl, Roland (2023). Charakterisierung des Erwartungswertes am Graphen der Verteilungsfunktion [Characterization of the expected value on the graph of the cumulative distribution function] (PDF). Technische Hochschule Brandenburg. p. 5. doi:10.25933/opus4-2986. Archived from the original on 2023-12-24.

nih.gov (Global: 4^th place; English: 4^th place)

pubmed.ncbi.nlm.nih.gov

Haldane, J. B. (1952). "Simple tests for bimodality and bitangentiality". Annals of Eugenics. 16 (4): 359–364. doi:10.1111/j.1469-1809.1951.tb02488.x. PMID 14953132.

nist.gov (Global: 355^th place; English: 454^th place)

nvlpubs.nist.gov

Savage, I. Richard. "Probability inequalities of the Tchebycheff type." Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics B 65 (1961): 211-222

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

Birnbaum, Z. W.; Raymond, J.; Zuckerman, H. S. (1947). "A Generalization of Tshebyshev's Inequality to Two Dimensions". The Annals of Mathematical Statistics. 18 (1): 70–79. doi:10.1214/aoms/1177730493. ISSN 0003-4851. MR 0019849. Zbl 0032.03402. Retrieved 7 October 2012.
Fink, A. M.; Jodeit, Max Jr. (1984). "On Chebyshev's other inequality". In Tong, Y. L.; Gupta, Shanti S. (eds.). Inequalities in Statistics and Probability. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Vol. 5. pp. 115–120. doi:10.1214/lnms/1215465637. ISBN 978-0-940600-04-1. MR 0789242. Retrieved 7 October 2012.

psu.edu (Global: 207^th place; English: 136^th place)

citeseerx.ist.psu.edu

Vandenberghe, L.; Boyd, S.; Comanor, K. (2007-01-01). "Generalized Chebyshev Bounds via Semidefinite Programming". SIAM Review. 49 (1): 52–64. Bibcode:2007SIAMR..49...52V. CiteSeerX 10.1.1.126.9105. doi:10.1137/S0036144504440543. ISSN 0036-1445.
Niculescu, Constantin P. (2001). "An extension of Chebyshev's inequality and its connection with Jensen's inequality". Journal of Inequalities and Applications. 6 (4): 451–462. CiteSeerX 10.1.1.612.7056. doi:10.1155/S1025583401000273. ISSN 1025-5834. Retrieved 6 October 2012.

researchgate.net (Global: 120^th place; English: 125^th place)

Grechuk, B., Molyboha, A., Zabarankin, M. (2010). Chebyshev Inequalities with Law Invariant Deviation Measures, Probability in the Engineering and Informational Sciences, 24(1), 145-170.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Ferentinos, K (1982). "On Tchebycheff type inequalities". Trabajos Estadıst Investigacion Oper. 33: 125–132. doi:10.1007/BF02888707. S2CID 123762564.
Stellato, Bartolomeo; Parys, Bart P. G. Van; Goulart, Paul J. (2016-05-31). "Multivariate Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 71 (2): 123–127. arXiv:1509.08398. doi:10.1080/00031305.2016.1186559. ISSN 0003-1305. S2CID 53407286.
Kabán, Ata (2012). "Non-parametric detection of meaningless distances in high dimensional data". Statistics and Computing. 22 (2): 375–85. doi:10.1007/s11222-011-9229-0. S2CID 6018114.
Beasley, T. Mark; Page, Grier P.; Brand, Jaap P. L.; Gadbury, Gary L.; Mountz, John D.; Allison, David B. (January 2004). "Chebyshev's inequality for nonparametric testing with small N and α in microarray research". Journal of the Royal Statistical Society. C (Applied Statistics). 53 (1): 95–108. doi:10.1111/j.1467-9876.2004.00428.x. ISSN 1467-9876. S2CID 122678278.
Nantell, Timothy J.; Price, Barbara (June 1979). "An Analytical Comparison of Variance and Semivariance Capital Market Theories". The Journal of Financial and Quantitative Analysis. 14 (2): 221–42. doi:10.2307/2330500. JSTOR 2330500. S2CID 154652959.
Pukelsheim, Friedrich (May 1994). "The Three Sigma Rule". The American Statistician. 48 (2): 88–91. doi:10.1080/00031305.1994.10476030. ISSN 0003-1305. S2CID 122587510.
DasGupta, A (2000). "Best constants in Chebychev inequalities with various applications". Metrika. 5 (1): 185–200. doi:10.1007/s184-000-8316-9. S2CID 121436601.
He, Simai; Zhang, Jiawei; Zhang, Shuzhong (2010). "Bounding probability of small deviation: a fourth moment approach". Mathematics of Operations Research. 35 (1): 208–232. doi:10.1287/moor.1090.0438. S2CID 11298475.

stackexchange.com (Global: 1,983^rd place; English: 1,330^th place)

math.stackexchange.com

"Error Term of Chebyshev inequality?". Mathematics Stack Exchange. Retrieved 2023-12-11.

stanford.edu (Global: 179^th place; English: 183^rd place)

www-cs-faculty.stanford.edu

Knuth, Donald (1997). The Art of Computer Programming: Fundamental Algorithms, Volume 1 (3rd ed.). Reading, Massachusetts: Addison–Wesley. ISBN 978-0-201-89683-1. Archived from the original on 26 February 2009. Retrieved 1 October 2012.

tandfonline.com (Global: 507^th place; English: 429^th place)

Godwin, H. J. (September 1955). "On Generalizations of Tchebychef's Inequality". Journal of the American Statistical Association. 50 (271): 923–945. doi:10.1080/01621459.1955.10501978. ISSN 0162-1459.
Pukelsheim, Friedrich (May 1994). "The Three Sigma Rule". The American Statistician. 48 (2): 88–91. doi:10.1080/00031305.1994.10476030. ISSN 0003-1305. S2CID 122587510.

unam.mx (Global: 769^th place; English: 1,834^th place)

emis.matem.unam.mx

Niculescu, Constantin P. (2001). "An extension of Chebyshev's inequality and its connection with Jensen's inequality". Journal of Inequalities and Applications. 6 (4): 451–462. CiteSeerX 10.1.1.612.7056. doi:10.1155/S1025583401000273. ISSN 1025-5834. Retrieved 6 October 2012.

utah.edu (Global: 2,446^th place; English: 1,661^st place)

math.utah.edu

Section 2.1 Archived April 30, 2015, at the Wayback Machine

vcu.edu (Global: 7,721^st place; English: 4,593^rd place)

people.vcu.edu

Conlon, J.; Dulá, J. H. "A geometric derivation and interpretation of Tchebyscheff's Inequality" (PDF). Retrieved 2 October 2012.

web.archive.org (Global: 1^st place; English: 1^st place)

Knuth, Donald (1997). The Art of Computer Programming: Fundamental Algorithms, Volume 1 (3rd ed.). Reading, Massachusetts: Addison–Wesley. ISBN 978-0-201-89683-1. Archived from the original on 26 February 2009. Retrieved 1 October 2012.
Uhl, Roland (2023). Charakterisierung des Erwartungswertes am Graphen der Verteilungsfunktion [Characterization of the expected value on the graph of the cumulative distribution function] (PDF). Technische Hochschule Brandenburg. p. 5. doi:10.25933/opus4-2986. Archived from the original on 2023-12-24.
Section 2.1 Archived April 30, 2015, at the Wayback Machine
Grimmett and Stirzaker, problem 7.11.9. Several proofs of this result can be found in Chebyshev's Inequalities Archived 2019-02-24 at the Wayback Machine by A. G. McDowell.

wiley.com (Global: 222^nd place; English: 297^th place)

Kotz, Samuel; Balakrishnan, N.; Johnson, Norman L. (2000). Continuous Multivariate Distributions, Volume 1, Models and Applications (2nd ed.). Boston [u.a.]: Houghton Mifflin. ISBN 978-0-471-18387-7. Retrieved 7 October 2012.

worldcat.org (Global: 5^th place; English: 5^th place)

search.worldcat.org

Selberg, Henrik L. (1940). "Zwei Ungleichungen zur Ergänzung des Tchebycheffschen Lemmas" [Two Inequalities Supplementing the Tchebycheff Lemma]. Skandinavisk Aktuarietidskrift (Scandinavian Actuarial Journal) (in German). 1940 (3–4): 121–125. doi:10.1080/03461238.1940.10404804. ISSN 0346-1238. OCLC 610399869.
Godwin, H. J. (September 1955). "On Generalizations of Tchebychef's Inequality". Journal of the American Statistical Association. 50 (271): 923–945. doi:10.1080/01621459.1955.10501978. ISSN 0162-1459.
Birnbaum, Z. W.; Raymond, J.; Zuckerman, H. S. (1947). "A Generalization of Tshebyshev's Inequality to Two Dimensions". The Annals of Mathematical Statistics. 18 (1): 70–79. doi:10.1214/aoms/1177730493. ISSN 0003-4851. MR 0019849. Zbl 0032.03402. Retrieved 7 October 2012.
Stellato, Bartolomeo; Parys, Bart P. G. Van; Goulart, Paul J. (2016-05-31). "Multivariate Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 71 (2): 123–127. arXiv:1509.08398. doi:10.1080/00031305.2016.1186559. ISSN 0003-1305. S2CID 53407286.
Vandenberghe, L.; Boyd, S.; Comanor, K. (2007-01-01). "Generalized Chebyshev Bounds via Semidefinite Programming". SIAM Review. 49 (1): 52–64. Bibcode:2007SIAMR..49...52V. CiteSeerX 10.1.1.126.9105. doi:10.1137/S0036144504440543. ISSN 0036-1445.
Saw, John G.; Yang, Mark C. K.; Mo, Tse Chin (1984). "Chebyshev Inequality with Estimated Mean and Variance". The American Statistician. 38 (2): 130–2. doi:10.2307/2683249. ISSN 0003-1305. JSTOR 2683249.
Beasley, T. Mark; Page, Grier P.; Brand, Jaap P. L.; Gadbury, Gary L.; Mountz, John D.; Allison, David B. (January 2004). "Chebyshev's inequality for nonparametric testing with small N and α in microarray research". Journal of the Royal Statistical Society. C (Applied Statistics). 53 (1): 95–108. doi:10.1111/j.1467-9876.2004.00428.x. ISSN 1467-9876. S2CID 122678278.
Berck, Peter; Hihn, Jairus M. (May 1982). "Using the Semivariance to Estimate Safety-First Rules". American Journal of Agricultural Economics. 64 (2): 298–300. doi:10.2307/1241139. ISSN 0002-9092. JSTOR 1241139.
Neave, Edwin H.; Ross, Michael N.; Yang, Jun (2009). "Distinguishing upside potential from downside risk". Management Research News. 32 (1): 26–36. doi:10.1108/01409170910922005. ISSN 0140-9174.
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Chebyshev's inequality (English Wikipedia)

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