Asymptotic results for jump probabilities associated to the multiple scan statistic
The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type r / k is a special pattern referring to success–failure strings of fixed length k that contain at least r -successes, where r , k are positive...
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| Veröffentlicht in: | Annals of the Institute of Statistical Mathematics 2018-10, Vol.70 (5), p.951-968 |
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| container_title | Annals of the Institute of Statistical Mathematics |
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| creator | Koutras, Markos V. Lyberopoulos, Demetrios P. |
| description | The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type
r
/
k
is a special pattern referring to success–failure strings of fixed length
k
that contain at least
r
-successes, where
r
,
k
are positive integers with
r
≤
k
. The multiple scan statistic
W
t
,
k
,
r
is defined as the enumerating random variable for the overlapping moving windows occurring until trial
t
which include a scan of type
r
/
k
. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from
ℓ
to
ℓ
+
1
(where
ℓ
is a nonnegative integer) in a finite time horizon. |
| doi_str_mv | 10.1007/s10463-017-0621-1 |
| format | Article |
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r
/
k
is a special pattern referring to success–failure strings of fixed length
k
that contain at least
r
-successes, where
r
,
k
are positive integers with
r
≤
k
. The multiple scan statistic
W
t
,
k
,
r
is defined as the enumerating random variable for the overlapping moving windows occurring until trial
t
which include a scan of type
r
/
k
. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from
ℓ
to
ℓ
+
1
(where
ℓ
is a nonnegative integer) in a finite time horizon.</description><identifier>ISSN: 0020-3157</identifier><identifier>EISSN: 1572-9052</identifier><identifier>DOI: 10.1007/s10463-017-0621-1</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Economics ; Finance ; Insurance ; Integers ; Management ; Mathematics ; Mathematics and Statistics ; Random variables ; Statistical analysis ; Statistics ; Statistics for Business ; Strings ; Upper bounds</subject><ispartof>Annals of the Institute of Statistical Mathematics, 2018-10, Vol.70 (5), p.951-968</ispartof><rights>The Institute of Statistical Mathematics, Tokyo 2017</rights><rights>Annals of the Institute of Statistical Mathematics is a copyright of Springer, (2017). All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-cc4003622e12df24679fb53081394b67b4bf369cef4c0529993a663d6ba0ce373</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10463-017-0621-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10463-017-0621-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Koutras, Markos V.</creatorcontrib><creatorcontrib>Lyberopoulos, Demetrios P.</creatorcontrib><title>Asymptotic results for jump probabilities associated to the multiple scan statistic</title><title>Annals of the Institute of Statistical Mathematics</title><addtitle>Ann Inst Stat Math</addtitle><description>The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type
r
/
k
is a special pattern referring to success–failure strings of fixed length
k
that contain at least
r
-successes, where
r
,
k
are positive integers with
r
≤
k
. The multiple scan statistic
W
t
,
k
,
r
is defined as the enumerating random variable for the overlapping moving windows occurring until trial
t
which include a scan of type
r
/
k
. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from
ℓ
to
ℓ
+
1
(where
ℓ
is a nonnegative integer) in a finite time horizon.</description><subject>Economics</subject><subject>Finance</subject><subject>Insurance</subject><subject>Integers</subject><subject>Management</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Random variables</subject><subject>Statistical analysis</subject><subject>Statistics</subject><subject>Statistics for Business</subject><subject>Strings</subject><subject>Upper bounds</subject><issn>0020-3157</issn><issn>1572-9052</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kD9PwzAQxS0EEqXwAdgsMRvu7NSpx6rin1SJAZgtx3XAVdIEnzv022MUBhamk06_9-7dY-wa4RYB6jtCqLQSgLUALVHgCZvhopbCwEKeshmABKHK5pxdEO0AQEklZ-x1Rcd-zEOOnqdAhy4Tb4fEd4d-5GMaGtfELuYYiDuiwUeXw5bngefPwPuCx7ELnLzbc8ouRypGl-ysdR2Fq985Z-8P92_rJ7F5eXxerzbCS73MwvuqpNBSBpTbVla6Nm2zULBEZapG103VtEobH9rKlyeMMcpprba6ceCDqtWc3Uy-JefXIVC2u-GQ9uWkRaMrgxprUyicKJ8GohRaO6bYu3S0CPanOzt1Z0t39qc7i0UjJw0Vdv8R0h_nf0XfCdJxuA</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Koutras, Markos V.</creator><creator>Lyberopoulos, Demetrios P.</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20181001</creationdate><title>Asymptotic results for jump probabilities associated to the multiple scan statistic</title><author>Koutras, Markos V. ; Lyberopoulos, Demetrios P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-cc4003622e12df24679fb53081394b67b4bf369cef4c0529993a663d6ba0ce373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Economics</topic><topic>Finance</topic><topic>Insurance</topic><topic>Integers</topic><topic>Management</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Random variables</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Statistics for Business</topic><topic>Strings</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Koutras, Markos V.</creatorcontrib><creatorcontrib>Lyberopoulos, Demetrios P.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Access via ABI/INFORM (ProQuest)</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</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>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</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 Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</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>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</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>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</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>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Annals of the Institute of Statistical Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Koutras, Markos V.</au><au>Lyberopoulos, Demetrios P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic results for jump probabilities associated to the multiple scan statistic</atitle><jtitle>Annals of the Institute of Statistical Mathematics</jtitle><stitle>Ann Inst Stat Math</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>70</volume><issue>5</issue><spage>951</spage><epage>968</epage><pages>951-968</pages><issn>0020-3157</issn><eissn>1572-9052</eissn><abstract>The concept of pattern arises in many applications comprising experimental trials with two or more possible outcomes in each trial. A binary scan of type
r
/
k
is a special pattern referring to success–failure strings of fixed length
k
that contain at least
r
-successes, where
r
,
k
are positive integers with
r
≤
k
. The multiple scan statistic
W
t
,
k
,
r
is defined as the enumerating random variable for the overlapping moving windows occurring until trial
t
which include a scan of type
r
/
k
. In the present work, we consider a sequence of independent binary trials with not necessarily equal probabilities of success and develop upper bounds for the probability of the event that the multiple scan statistic will perform a jump from
ℓ
to
ℓ
+
1
(where
ℓ
is a nonnegative integer) in a finite time horizon.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s10463-017-0621-1</doi><tpages>18</tpages></addata></record> |
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| identifier | ISSN: 0020-3157 |
| ispartof | Annals of the Institute of Statistical Mathematics, 2018-10, Vol.70 (5), p.951-968 |
| issn | 0020-3157 1572-9052 |
| language | eng |
| recordid | cdi_proquest_journals_1964916179 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; SpringerNature Journals |
| subjects | Economics Finance Insurance Integers Management Mathematics Mathematics and Statistics Random variables Statistical analysis Statistics Statistics for Business Strings Upper bounds |
| title | Asymptotic results for jump probabilities associated to the multiple scan statistic |
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