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Best-possible bounds on sets of bivariate distribution functions
The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fréchet–Hoeffding inequality: If H denotes the joint distribution function of random variables X and Y whose margins are F and G, respectively, then max(0, F( x)+ G( y)−1)⩽ H( x, y)⩽min( F(...
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| Published in: | Journal of multivariate analysis 2004-08, Vol.90 (2), p.348-358 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c466t-c27c14fa99604055a7dabe6a512d87c9e7b72125ea8daface8716c295102271d3 |
| container_end_page | 358 |
| container_issue | 2 |
| container_start_page | 348 |
| container_title | Journal of multivariate analysis |
| container_volume | 90 |
| creator | Nelsen, Roger B Molina, José Juan Quesada Lallena, José Antonio Rodrı́guez Flores, Manuel Úbeda |
| description | The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fréchet–Hoeffding inequality: If
H denotes the joint distribution function of random variables
X and
Y whose margins are
F and
G, respectively, then max(0,
F(
x)+
G(
y)−1)⩽
H(
x,
y)⩽min(
F(
x),
G(
y)) for all
x,
y in [−∞,∞]. In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function
H with given margins
F and
G when the values of
H are known at quartiles of
X and
Y. |
| doi_str_mv | 10.1016/j.jmva.2003.09.002 |
| format | article |
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H denotes the joint distribution function of random variables
X and
Y whose margins are
F and
G, respectively, then max(0,
F(
x)+
G(
y)−1)⩽
H(
x,
y)⩽min(
F(
x),
G(
y)) for all
x,
y in [−∞,∞]. In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function
H with given margins
F and
G when the values of
H are known at quartiles of
X and
Y.</description><identifier>ISSN: 0047-259X</identifier><identifier>EISSN: 1095-7243</identifier><identifier>DOI: 10.1016/j.jmva.2003.09.002</identifier><identifier>CODEN: JMVAAI</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Bounds ; Bounds Copulas Distribution functions Kendall's tau Quartiles Quasi-copulas ; Copulas ; Distribution functions ; Exact sciences and technology ; Kendall's tau ; Mathematics ; Multivariate analysis ; Probability and statistics ; Quartiles ; Quasi-copulas ; Random variables ; Sciences and techniques of general use ; Statistics ; Studies</subject><ispartof>Journal of multivariate analysis, 2004-08, Vol.90 (2), p.348-358</ispartof><rights>2003 Elsevier Inc.</rights><rights>2004 INIST-CNRS</rights><rights>Copyright Taylor & Francis Group Aug 2004</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c466t-c27c14fa99604055a7dabe6a512d87c9e7b72125ea8daface8716c295102271d3</citedby><cites>FETCH-LOGICAL-c466t-c27c14fa99604055a7dabe6a512d87c9e7b72125ea8daface8716c295102271d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27900,27901</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15947739$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeejmvana/v_3a90_3ay_3a2004_3ai_3a2_3ap_3a348-358.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Nelsen, Roger B</creatorcontrib><creatorcontrib>Molina, José Juan Quesada</creatorcontrib><creatorcontrib>Lallena, José Antonio Rodrı́guez</creatorcontrib><creatorcontrib>Flores, Manuel Úbeda</creatorcontrib><title>Best-possible bounds on sets of bivariate distribution functions</title><title>Journal of multivariate analysis</title><description>The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fréchet–Hoeffding inequality: If
H denotes the joint distribution function of random variables
X and
Y whose margins are
F and
G, respectively, then max(0,
F(
x)+
G(
y)−1)⩽
H(
x,
y)⩽min(
F(
x),
G(
y)) for all
x,
y in [−∞,∞]. In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function
H with given margins
F and
G when the values of
H are known at quartiles of
X and
Y.</description><subject>Bounds</subject><subject>Bounds Copulas Distribution functions Kendall's tau Quartiles Quasi-copulas</subject><subject>Copulas</subject><subject>Distribution functions</subject><subject>Exact sciences and technology</subject><subject>Kendall's tau</subject><subject>Mathematics</subject><subject>Multivariate analysis</subject><subject>Probability and statistics</subject><subject>Quartiles</subject><subject>Quasi-copulas</subject><subject>Random variables</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>Studies</subject><issn>0047-259X</issn><issn>1095-7243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><recordid>eNp9UMGK1TAUDaLgc_QHXBXBZTs3adI04EId1FEG3Ci4C7fpLaa819akfTB_P7e8QXcuTs6FnHNzcoR4LaGSIJvrsRpPZ6wUQF2BqwDUE3GQ4Expla6figOAtqUy7tdz8SLnEUBKY_VBvP9IeS2XOefYHano5m3qczFPRaaVeSi6eMYUcaWij3lNsdvWyNfDNoV9yC_FswGPmV498pX4-fnTj5vb8u77l683H-7KoJtmLYOyQeoBnWtAgzFoe-yoQSNV39rgyHZWSWUI2x4HDNRa2QTljASlrOzrK_HmsndJ85-NQ_tx3tLET3ol28YpMA2L1EUUEv8o0eCXFE-Y7r0EvxflR78X5feiPDjPRbHp28WUaKHw10FEu3RCf_Y1OuDjnsFOzRT3kbEwat362rT-93riZW8fY2IOeBwSTiHmfzGM09bWjnXvLjrizs6Rks8h0hSoj4nC6vs5_i_zA3KHl3o</recordid><startdate>20040801</startdate><enddate>20040801</enddate><creator>Nelsen, Roger B</creator><creator>Molina, José Juan Quesada</creator><creator>Lallena, José Antonio Rodrı́guez</creator><creator>Flores, Manuel Úbeda</creator><general>Elsevier Inc</general><general>Elsevier</general><general>Taylor & Francis LLC</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20040801</creationdate><title>Best-possible bounds on sets of bivariate distribution functions</title><author>Nelsen, Roger B ; Molina, José Juan Quesada ; Lallena, José Antonio Rodrı́guez ; Flores, Manuel Úbeda</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c466t-c27c14fa99604055a7dabe6a512d87c9e7b72125ea8daface8716c295102271d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Bounds</topic><topic>Bounds Copulas Distribution functions Kendall's tau Quartiles Quasi-copulas</topic><topic>Copulas</topic><topic>Distribution functions</topic><topic>Exact sciences and technology</topic><topic>Kendall's tau</topic><topic>Mathematics</topic><topic>Multivariate analysis</topic><topic>Probability and statistics</topic><topic>Quartiles</topic><topic>Quasi-copulas</topic><topic>Random variables</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nelsen, Roger B</creatorcontrib><creatorcontrib>Molina, José Juan Quesada</creatorcontrib><creatorcontrib>Lallena, José Antonio Rodrı́guez</creatorcontrib><creatorcontrib>Flores, Manuel Úbeda</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Journal of multivariate analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nelsen, Roger B</au><au>Molina, José Juan Quesada</au><au>Lallena, José Antonio Rodrı́guez</au><au>Flores, Manuel Úbeda</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Best-possible bounds on sets of bivariate distribution functions</atitle><jtitle>Journal of multivariate analysis</jtitle><date>2004-08-01</date><risdate>2004</risdate><volume>90</volume><issue>2</issue><spage>348</spage><epage>358</epage><pages>348-358</pages><issn>0047-259X</issn><eissn>1095-7243</eissn><coden>JMVAAI</coden><abstract>The fundamental best-possible bounds inequality for bivariate distribution functions with given margins is the Fréchet–Hoeffding inequality: If
H denotes the joint distribution function of random variables
X and
Y whose margins are
F and
G, respectively, then max(0,
F(
x)+
G(
y)−1)⩽
H(
x,
y)⩽min(
F(
x),
G(
y)) for all
x,
y in [−∞,∞]. In this paper we employ copulas and quasi-copulas to find similar best-possible bounds on arbitrary sets of bivariate distribution functions with given margins. As an application, we discuss bounds for a bivariate distribution function
H with given margins
F and
G when the values of
H are known at quartiles of
X and
Y.</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jmva.2003.09.002</doi><tpages>11</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of multivariate analysis, 2004-08, Vol.90 (2), p.348-358 |
| issn | 0047-259X 1095-7243 |
| language | eng |
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| source | ScienceDirect Journals |
| subjects | Bounds Bounds Copulas Distribution functions Kendall's tau Quartiles Quasi-copulas Copulas Distribution functions Exact sciences and technology Kendall's tau Mathematics Multivariate analysis Probability and statistics Quartiles Quasi-copulas Random variables Sciences and techniques of general use Statistics Studies |
| title | Best-possible bounds on sets of bivariate distribution functions |
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