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Quasi-copulas with a given sub-diagonal section
As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula Q , max { x + y − 1 , 0 } ≤ Q ( x , y ) ≤ min { x , y } for all x , y ∈ [ 0 , 1 ] . Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along thei...
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| Published in: | Nonlinear analysis 2008-12, Vol.69 (12), p.4654-4673 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373 |
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| cites | cdi_FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373 |
| container_end_page | 4673 |
| container_issue | 12 |
| container_start_page | 4654 |
| container_title | Nonlinear analysis |
| container_volume | 69 |
| creator | Quesada-Molina, José Juan Saminger-Platz, Susanne Sempi, Carlo |
| description | As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula
Q
,
max
{
x
+
y
−
1
,
0
}
≤
Q
(
x
,
y
)
≤
min
{
x
,
y
}
for all
x
,
y
∈
[
0
,
1
]
. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points
(
x
0
,
0
)
and
(
1
,
1
−
x
0
)
for
x
0
∈
]
0
,
1
[
. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section. |
| doi_str_mv | 10.1016/j.na.2007.11.021 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_35586119</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0362546X07007754</els_id><sourcerecordid>35586119</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373</originalsourceid><addsrcrecordid>eNp1kL9PwzAQhS0EEqWwM2aBLemdndgJG6r4JVVCSCCxWa5zKa5Sp9hJEf89qYrYmG753nu6j7FLhAwB5WydeZNxAJUhZsDxiE2wVCItOBbHbAJC8rTI5fspO4txDQCohJyw2ctgoktttx1aE5Mv138kJlm5HfkkDsu0dmbVedMmkWzvOn_OThrTRrr4vVP2dn_3On9MF88PT_PbRWpFUfRpoeq8FCIXEqioVVOVQBI4NRWQLalGToCNUpgrpEqBWpKyqi4rTigbocSUXR96t6H7HCj2euOipbY1nroh6nGllIjVCMIBtKGLMVCjt8FtTPjWCHpvRq-1N3pvRiPq0cwYufrtNtGatgnGWxf_chzKKuc5jNzNgaPx0Z2joKN15C3VLow2dN25_0d-ACFVdd4</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>35586119</pqid></control><display><type>article</type><title>Quasi-copulas with a given sub-diagonal section</title><source>ScienceDirect Freedom Collection</source><source>Backfile Package - Mathematics (Legacy) [YMT]</source><creator>Quesada-Molina, José Juan ; Saminger-Platz, Susanne ; Sempi, Carlo</creator><creatorcontrib>Quesada-Molina, José Juan ; Saminger-Platz, Susanne ; Sempi, Carlo</creatorcontrib><description>As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula
Q
,
max
{
x
+
y
−
1
,
0
}
≤
Q
(
x
,
y
)
≤
min
{
x
,
y
}
for all
x
,
y
∈
[
0
,
1
]
. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points
(
x
0
,
0
)
and
(
1
,
1
−
x
0
)
for
x
0
∈
]
0
,
1
[
. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2007.11.021</identifier><identifier>CODEN: NOANDD</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Copula ; Exact sciences and technology ; Mathematical analysis ; Mathematics ; Quasi-copula ; Sciences and techniques of general use ; Sub-diagonal (section)</subject><ispartof>Nonlinear analysis, 2008-12, Vol.69 (12), p.4654-4673</ispartof><rights>2007 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373</citedby><cites>FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0362546X07007754$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3551,27903,27904,45981</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20894240$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Quesada-Molina, José Juan</creatorcontrib><creatorcontrib>Saminger-Platz, Susanne</creatorcontrib><creatorcontrib>Sempi, Carlo</creatorcontrib><title>Quasi-copulas with a given sub-diagonal section</title><title>Nonlinear analysis</title><description>As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula
Q
,
max
{
x
+
y
−
1
,
0
}
≤
Q
(
x
,
y
)
≤
min
{
x
,
y
}
for all
x
,
y
∈
[
0
,
1
]
. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points
(
x
0
,
0
)
and
(
1
,
1
−
x
0
)
for
x
0
∈
]
0
,
1
[
. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.</description><subject>Copula</subject><subject>Exact sciences and technology</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Quasi-copula</subject><subject>Sciences and techniques of general use</subject><subject>Sub-diagonal (section)</subject><issn>0362-546X</issn><issn>1873-5215</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp1kL9PwzAQhS0EEqWwM2aBLemdndgJG6r4JVVCSCCxWa5zKa5Sp9hJEf89qYrYmG753nu6j7FLhAwB5WydeZNxAJUhZsDxiE2wVCItOBbHbAJC8rTI5fspO4txDQCohJyw2ctgoktttx1aE5Mv138kJlm5HfkkDsu0dmbVedMmkWzvOn_OThrTRrr4vVP2dn_3On9MF88PT_PbRWpFUfRpoeq8FCIXEqioVVOVQBI4NRWQLalGToCNUpgrpEqBWpKyqi4rTigbocSUXR96t6H7HCj2euOipbY1nroh6nGllIjVCMIBtKGLMVCjt8FtTPjWCHpvRq-1N3pvRiPq0cwYufrtNtGatgnGWxf_chzKKuc5jNzNgaPx0Z2joKN15C3VLow2dN25_0d-ACFVdd4</recordid><startdate>20081215</startdate><enddate>20081215</enddate><creator>Quesada-Molina, José Juan</creator><creator>Saminger-Platz, Susanne</creator><creator>Sempi, Carlo</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20081215</creationdate><title>Quasi-copulas with a given sub-diagonal section</title><author>Quesada-Molina, José Juan ; Saminger-Platz, Susanne ; Sempi, Carlo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-57d48334360e5d7f980e602ef90ec8ed12e01f771471e9707be7c7d892e16f373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Copula</topic><topic>Exact sciences and technology</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Quasi-copula</topic><topic>Sciences and techniques of general use</topic><topic>Sub-diagonal (section)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Quesada-Molina, José Juan</creatorcontrib><creatorcontrib>Saminger-Platz, Susanne</creatorcontrib><creatorcontrib>Sempi, Carlo</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Quesada-Molina, José Juan</au><au>Saminger-Platz, Susanne</au><au>Sempi, Carlo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quasi-copulas with a given sub-diagonal section</atitle><jtitle>Nonlinear analysis</jtitle><date>2008-12-15</date><risdate>2008</risdate><volume>69</volume><issue>12</issue><spage>4654</spage><epage>4673</epage><pages>4654-4673</pages><issn>0362-546X</issn><eissn>1873-5215</eissn><coden>NOANDD</coden><abstract>As is well known, the Fréchet–Hoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-) copula
Q
,
max
{
x
+
y
−
1
,
0
}
≤
Q
(
x
,
y
)
≤
min
{
x
,
y
}
for all
x
,
y
∈
[
0
,
1
]
. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points
(
x
0
,
0
)
and
(
1
,
1
−
x
0
)
for
x
0
∈
]
0
,
1
[
. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.na.2007.11.021</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0362-546X |
| ispartof | Nonlinear analysis, 2008-12, Vol.69 (12), p.4654-4673 |
| issn | 0362-546X 1873-5215 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_35586119 |
| source | ScienceDirect Freedom Collection; Backfile Package - Mathematics (Legacy) [YMT] |
| subjects | Copula Exact sciences and technology Mathematical analysis Mathematics Quasi-copula Sciences and techniques of general use Sub-diagonal (section) |
| title | Quasi-copulas with a given sub-diagonal section |
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