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Some asymptotic results on extremes of incomplete samples
Let X 1 , X 2 , ⋯ be a sequence of independent and identically distributed random variables and M n = max { X 1 , X 2 , ⋯ , X n }. Suppose that some of the random variables X 1 , X 2 , ⋯ , X n can be observed and denote by the maximum of the observed random variables from the set { X 1 , X 2 , ⋯ ,...
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| Published in: | Extremes (Boston) 2012-09, Vol.15 (3), p.319-332 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c316t-6b6a487df33fd33d0d8e11367ecc511fdccfd7ae7e13255e3f4d0e373e62e1703 |
| container_end_page | 332 |
| container_issue | 3 |
| container_start_page | 319 |
| container_title | Extremes (Boston) |
| container_volume | 15 |
| creator | Tan, Zhongquan Wang, Yuebao |
| description | Let
X
1
,
X
2
, ⋯ be a sequence of independent and identically distributed random variables and
M
n
= max {
X
1
,
X
2
, ⋯ ,
X
n
}. Suppose that some of the random variables
X
1
,
X
2
, ⋯ ,
X
n
can be observed and denote by
the maximum of the observed random variables from the set {
X
1
,
X
2
, ⋯ ,
X
n
}. The limiting distribution of random vector
is derived. The result is also extended to the case of stationary Gaussian sequences. In the end, the almost sure limit theorem on
for a sequence of independent and identically distributed random variables is proved. |
| doi_str_mv | 10.1007/s10687-011-0140-z |
| format | article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1039256997</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2759527081</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-6b6a487df33fd33d0d8e11367ecc511fdccfd7ae7e13255e3f4d0e373e62e1703</originalsourceid><addsrcrecordid>eNp1kE1LAzEQhoMoWKs_wNuC52hms0k2Ryl-QcGDCt7CmkykpbtZkxRsf70p68GLh2Hew_PMwEvIJbBrYEzdJGCyVZQBlGkY3R-RGQhVUw3i_bhk3koKWutTcpbSmhUHpJgR_RJ6rLq068cc8spWEdN2k1MVhgq_c8QeS_bVarChHzeYsUrdIaRzcuK7TcKL3z0nb_d3r4tHunx-eFrcLqnlIDOVH7JrWuU8595x7phrEYBLhdYKAO-s9U51qBB4LQRy3ziGXHGUNYJifE6uprtjDF9bTNmswzYO5aUBxnUtpNaqUDBRNoaUInozxlXfxV2BzKEhMzVkSkPm0JDZF6eenFTY4RPj38v_ST_kUGnQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1039256997</pqid></control><display><type>article</type><title>Some asymptotic results on extremes of incomplete samples</title><source>Business Source Ultimate</source><source>ABI/INFORM Global</source><source>Springer Nature</source><creator>Tan, Zhongquan ; Wang, Yuebao</creator><creatorcontrib>Tan, Zhongquan ; Wang, Yuebao</creatorcontrib><description>Let
X
1
,
X
2
, ⋯ be a sequence of independent and identically distributed random variables and
M
n
= max {
X
1
,
X
2
, ⋯ ,
X
n
}. Suppose that some of the random variables
X
1
,
X
2
, ⋯ ,
X
n
can be observed and denote by
the maximum of the observed random variables from the set {
X
1
,
X
2
, ⋯ ,
X
n
}. The limiting distribution of random vector
is derived. The result is also extended to the case of stationary Gaussian sequences. In the end, the almost sure limit theorem on
for a sequence of independent and identically distributed random variables is proved.</description><identifier>ISSN: 1386-1999</identifier><identifier>EISSN: 1572-915X</identifier><identifier>DOI: 10.1007/s10687-011-0140-z</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Air pollution ; Asymptotic methods ; Civil Engineering ; Economics ; Environmental Management ; Finance ; Hydrogeology ; Insurance ; Management ; Mathematical models ; Mathematics and Statistics ; Quality Control ; Random variables ; Reliability ; Safety and Risk ; Statistics ; Statistics for Business ; Theory</subject><ispartof>Extremes (Boston), 2012-09, Vol.15 (3), p.319-332</ispartof><rights>Springer Science+Business Media, LLC 2011</rights><rights>Springer Science+Business Media, LLC 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-6b6a487df33fd33d0d8e11367ecc511fdccfd7ae7e13255e3f4d0e373e62e1703</citedby><cites>FETCH-LOGICAL-c316t-6b6a487df33fd33d0d8e11367ecc511fdccfd7ae7e13255e3f4d0e373e62e1703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1039256997/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1039256997?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,11687,27923,27924,36059,44362,74766</link.rule.ids></links><search><creatorcontrib>Tan, Zhongquan</creatorcontrib><creatorcontrib>Wang, Yuebao</creatorcontrib><title>Some asymptotic results on extremes of incomplete samples</title><title>Extremes (Boston)</title><addtitle>Extremes</addtitle><description>Let
X
1
,
X
2
, ⋯ be a sequence of independent and identically distributed random variables and
M
n
= max {
X
1
,
X
2
, ⋯ ,
X
n
}. Suppose that some of the random variables
X
1
,
X
2
, ⋯ ,
X
n
can be observed and denote by
the maximum of the observed random variables from the set {
X
1
,
X
2
, ⋯ ,
X
n
}. The limiting distribution of random vector
is derived. The result is also extended to the case of stationary Gaussian sequences. In the end, the almost sure limit theorem on
for a sequence of independent and identically distributed random variables is proved.</description><subject>Air pollution</subject><subject>Asymptotic methods</subject><subject>Civil Engineering</subject><subject>Economics</subject><subject>Environmental Management</subject><subject>Finance</subject><subject>Hydrogeology</subject><subject>Insurance</subject><subject>Management</subject><subject>Mathematical models</subject><subject>Mathematics and Statistics</subject><subject>Quality Control</subject><subject>Random variables</subject><subject>Reliability</subject><subject>Safety and Risk</subject><subject>Statistics</subject><subject>Statistics for Business</subject><subject>Theory</subject><issn>1386-1999</issn><issn>1572-915X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>M0C</sourceid><recordid>eNp1kE1LAzEQhoMoWKs_wNuC52hms0k2Ryl-QcGDCt7CmkykpbtZkxRsf70p68GLh2Hew_PMwEvIJbBrYEzdJGCyVZQBlGkY3R-RGQhVUw3i_bhk3koKWutTcpbSmhUHpJgR_RJ6rLq068cc8spWEdN2k1MVhgq_c8QeS_bVarChHzeYsUrdIaRzcuK7TcKL3z0nb_d3r4tHunx-eFrcLqnlIDOVH7JrWuU8595x7phrEYBLhdYKAO-s9U51qBB4LQRy3ziGXHGUNYJifE6uprtjDF9bTNmswzYO5aUBxnUtpNaqUDBRNoaUInozxlXfxV2BzKEhMzVkSkPm0JDZF6eenFTY4RPj38v_ST_kUGnQ</recordid><startdate>20120901</startdate><enddate>20120901</enddate><creator>Tan, Zhongquan</creator><creator>Wang, Yuebao</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>0U~</scope><scope>1-H</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8C1</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>FYUFA</scope><scope>F~G</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20120901</creationdate><title>Some asymptotic results on extremes of incomplete samples</title><author>Tan, Zhongquan ; Wang, Yuebao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-6b6a487df33fd33d0d8e11367ecc511fdccfd7ae7e13255e3f4d0e373e62e1703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Air pollution</topic><topic>Asymptotic methods</topic><topic>Civil Engineering</topic><topic>Economics</topic><topic>Environmental Management</topic><topic>Finance</topic><topic>Hydrogeology</topic><topic>Insurance</topic><topic>Management</topic><topic>Mathematical models</topic><topic>Mathematics and Statistics</topic><topic>Quality Control</topic><topic>Random variables</topic><topic>Reliability</topic><topic>Safety and Risk</topic><topic>Statistics</topic><topic>Statistics for Business</topic><topic>Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tan, Zhongquan</creatorcontrib><creatorcontrib>Wang, Yuebao</creatorcontrib><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Public Health Database</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Business Premium Collection (Alumni)</collection><collection>Health Research Premium Collection</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Extremes (Boston)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Tan, Zhongquan</au><au>Wang, Yuebao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some asymptotic results on extremes of incomplete samples</atitle><jtitle>Extremes (Boston)</jtitle><stitle>Extremes</stitle><date>2012-09-01</date><risdate>2012</risdate><volume>15</volume><issue>3</issue><spage>319</spage><epage>332</epage><pages>319-332</pages><issn>1386-1999</issn><eissn>1572-915X</eissn><abstract>Let
X
1
,
X
2
, ⋯ be a sequence of independent and identically distributed random variables and
M
n
= max {
X
1
,
X
2
, ⋯ ,
X
n
}. Suppose that some of the random variables
X
1
,
X
2
, ⋯ ,
X
n
can be observed and denote by
the maximum of the observed random variables from the set {
X
1
,
X
2
, ⋯ ,
X
n
}. The limiting distribution of random vector
is derived. The result is also extended to the case of stationary Gaussian sequences. In the end, the almost sure limit theorem on
for a sequence of independent and identically distributed random variables is proved.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10687-011-0140-z</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1386-1999 |
| ispartof | Extremes (Boston), 2012-09, Vol.15 (3), p.319-332 |
| issn | 1386-1999 1572-915X |
| language | eng |
| recordid | cdi_proquest_journals_1039256997 |
| source | Business Source Ultimate; ABI/INFORM Global; Springer Nature |
| subjects | Air pollution Asymptotic methods Civil Engineering Economics Environmental Management Finance Hydrogeology Insurance Management Mathematical models Mathematics and Statistics Quality Control Random variables Reliability Safety and Risk Statistics Statistics for Business Theory |
| title | Some asymptotic results on extremes of incomplete samples |
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