Approximations for a Three Dimensional Scan Statistic
Let X ijk ,1 ≤ i ≤ N 1 ,1 ≤ j ≤ N 2 , 1 ≤ k ≤ N 3 be a sequence of independent and identically distributed 0 − 1 Bernoulli trials. X ijk = 1 if an event has occurred at the i , j , k th location in a three dimensional rectangular region and X ijk = 0, otherwise. For 2 ≤ m j ≤ N j − 1,...
Gespeichert in:
| Veröffentlicht in: | Methodology and computing in applied probability 2010-12, Vol.12 (4), p.731-747 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 747 |
|---|---|
| container_issue | 4 |
| container_start_page | 731 |
| container_title | Methodology and computing in applied probability |
| container_volume | 12 |
| creator | Glaz, Joseph Guerriero, Marco Sen, Rohini |
| description | Let
X
ijk
,1 ≤
i
≤
N
1
,1 ≤
j
≤
N
2
, 1 ≤
k
≤
N
3
be a sequence of independent and identically distributed 0 − 1 Bernoulli trials.
X
ijk
= 1 if an event has occurred at the
i
,
j
,
k
th
location in a three dimensional rectangular region and
X
ijk
= 0, otherwise. For 2 ≤
m
j
≤
N
j
− 1,1 ≤
j
≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any
m
1
×
m
2
×
m
3
rectangular sub-region in the entire
N
1
×
N
2
×
N
3
rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations and their use in testing for randomness. |
| doi_str_mv | 10.1007/s11009-009-9156-0 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_861546957</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2155165781</sourcerecordid><originalsourceid>FETCH-LOGICAL-c347t-97a6edba0fcf2305c25b8211b305fe068e5cba18a168e0cfadf9e45529aa35fd3</originalsourceid><addsrcrecordid>eNp1kE9LxDAQxYMouK5-AG_Fi6doJmma5risf2HBw67nkGYT7dJt10wL-u1NqSAIHoZ5DL83zDxCLoHdAGPqFiE1TcfSIAvKjsgMpBJUKRDHSYtSUVnmcErOEHeMcZAinxG5OBxi91nvbV93LWahi5nNNu_R--yu3vsW09g22drZNlv3icK-dufkJNgG_cVPn5PXh_vN8omuXh6fl4sVdSJXPdXKFn5bWRZc4IJJx2VVcoAq6eBZUXrpKgulhSSZC3YbtM-l5NpaIcNWzMn1tDfd-DF47M2-Ruebxra-G9CUBci80OnPObn6Q-66IabL0ShZFEorrhMEE-Rihxh9MIeYPo9fBpgZYzRTjGasMUbDkodPHkxs--bj7-L_Td8FvnR6</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>756679729</pqid></control><display><type>article</type><title>Approximations for a Three Dimensional Scan Statistic</title><source>SpringerNature Journals</source><source>EBSCOhost Business Source Complete</source><creator>Glaz, Joseph ; Guerriero, Marco ; Sen, Rohini</creator><creatorcontrib>Glaz, Joseph ; Guerriero, Marco ; Sen, Rohini</creatorcontrib><description>Let
X
ijk
,1 ≤
i
≤
N
1
,1 ≤
j
≤
N
2
, 1 ≤
k
≤
N
3
be a sequence of independent and identically distributed 0 − 1 Bernoulli trials.
X
ijk
= 1 if an event has occurred at the
i
,
j
,
k
th
location in a three dimensional rectangular region and
X
ijk
= 0, otherwise. For 2 ≤
m
j
≤
N
j
− 1,1 ≤
j
≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any
m
1
×
m
2
×
m
3
rectangular sub-region in the entire
N
1
×
N
2
×
N
3
rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations and their use in testing for randomness.</description><identifier>ISSN: 1387-5841</identifier><identifier>EISSN: 1573-7713</identifier><identifier>DOI: 10.1007/s11009-009-9156-0</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Accuracy ; Approximation ; Business and Management ; Computation ; Economics ; Electrical Engineering ; Life Sciences ; Mathematical models ; Mathematics and Statistics ; Methodology ; Position (location) ; Probability ; Randomness ; Statistics ; Studies</subject><ispartof>Methodology and computing in applied probability, 2010-12, Vol.12 (4), p.731-747</ispartof><rights>Springer Science+Business Media, LLC 2009</rights><rights>Springer Science+Business Media, LLC 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-97a6edba0fcf2305c25b8211b305fe068e5cba18a168e0cfadf9e45529aa35fd3</citedby><cites>FETCH-LOGICAL-c347t-97a6edba0fcf2305c25b8211b305fe068e5cba18a168e0cfadf9e45529aa35fd3</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/s11009-009-9156-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11009-009-9156-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Glaz, Joseph</creatorcontrib><creatorcontrib>Guerriero, Marco</creatorcontrib><creatorcontrib>Sen, Rohini</creatorcontrib><title>Approximations for a Three Dimensional Scan Statistic</title><title>Methodology and computing in applied probability</title><addtitle>Methodol Comput Appl Probab</addtitle><description>Let
X
ijk
,1 ≤
i
≤
N
1
,1 ≤
j
≤
N
2
, 1 ≤
k
≤
N
3
be a sequence of independent and identically distributed 0 − 1 Bernoulli trials.
X
ijk
= 1 if an event has occurred at the
i
,
j
,
k
th
location in a three dimensional rectangular region and
X
ijk
= 0, otherwise. For 2 ≤
m
j
≤
N
j
− 1,1 ≤
j
≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any
m
1
×
m
2
×
m
3
rectangular sub-region in the entire
N
1
×
N
2
×
N
3
rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations and their use in testing for randomness.</description><subject>Accuracy</subject><subject>Approximation</subject><subject>Business and Management</subject><subject>Computation</subject><subject>Economics</subject><subject>Electrical Engineering</subject><subject>Life Sciences</subject><subject>Mathematical models</subject><subject>Mathematics and Statistics</subject><subject>Methodology</subject><subject>Position (location)</subject><subject>Probability</subject><subject>Randomness</subject><subject>Statistics</subject><subject>Studies</subject><issn>1387-5841</issn><issn>1573-7713</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kE9LxDAQxYMouK5-AG_Fi6doJmma5risf2HBw67nkGYT7dJt10wL-u1NqSAIHoZ5DL83zDxCLoHdAGPqFiE1TcfSIAvKjsgMpBJUKRDHSYtSUVnmcErOEHeMcZAinxG5OBxi91nvbV93LWahi5nNNu_R--yu3vsW09g22drZNlv3icK-dufkJNgG_cVPn5PXh_vN8omuXh6fl4sVdSJXPdXKFn5bWRZc4IJJx2VVcoAq6eBZUXrpKgulhSSZC3YbtM-l5NpaIcNWzMn1tDfd-DF47M2-Ruebxra-G9CUBci80OnPObn6Q-66IabL0ShZFEorrhMEE-Rihxh9MIeYPo9fBpgZYzRTjGasMUbDkodPHkxs--bj7-L_Td8FvnR6</recordid><startdate>20101201</startdate><enddate>20101201</enddate><creator>Glaz, Joseph</creator><creator>Guerriero, Marco</creator><creator>Sen, Rohini</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>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</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>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L.0</scope><scope>L6V</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</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>PYYUZ</scope><scope>Q9U</scope><scope>7SC</scope><scope>8FD</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20101201</creationdate><title>Approximations for a Three Dimensional Scan Statistic</title><author>Glaz, Joseph ; Guerriero, Marco ; Sen, Rohini</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-97a6edba0fcf2305c25b8211b305fe068e5cba18a168e0cfadf9e45529aa35fd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Accuracy</topic><topic>Approximation</topic><topic>Business and Management</topic><topic>Computation</topic><topic>Economics</topic><topic>Electrical Engineering</topic><topic>Life Sciences</topic><topic>Mathematical models</topic><topic>Mathematics and Statistics</topic><topic>Methodology</topic><topic>Position (location)</topic><topic>Probability</topic><topic>Randomness</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Glaz, Joseph</creatorcontrib><creatorcontrib>Guerriero, Marco</creatorcontrib><creatorcontrib>Sen, Rohini</creatorcontrib><collection>CrossRef</collection><collection>Global News & ABI/Inform Professional</collection><collection>Trade PRO</collection><collection>ProQuest Central (Corporate)</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>ProQuest Pharma Collection</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 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>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>ABI/INFORM Professional Standard</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>Science Database</collection><collection>Engineering Database</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>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</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>Methodology and computing in applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Glaz, Joseph</au><au>Guerriero, Marco</au><au>Sen, Rohini</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximations for a Three Dimensional Scan Statistic</atitle><jtitle>Methodology and computing in applied probability</jtitle><stitle>Methodol Comput Appl Probab</stitle><date>2010-12-01</date><risdate>2010</risdate><volume>12</volume><issue>4</issue><spage>731</spage><epage>747</epage><pages>731-747</pages><issn>1387-5841</issn><eissn>1573-7713</eissn><abstract>Let
X
ijk
,1 ≤
i
≤
N
1
,1 ≤
j
≤
N
2
, 1 ≤
k
≤
N
3
be a sequence of independent and identically distributed 0 − 1 Bernoulli trials.
X
ijk
= 1 if an event has occurred at the
i
,
j
,
k
th
location in a three dimensional rectangular region and
X
ijk
= 0, otherwise. For 2 ≤
m
j
≤
N
j
− 1,1 ≤
j
≤ 3, a three dimensional discrete scan statistic is defined as the maximum number of events in any
m
1
×
m
2
×
m
3
rectangular sub-region in the entire
N
1
×
N
2
×
N
3
rectangular region. In this article, a product-type approximation and three Poisson approximations are derived for the distribution of this three dimensional scan statistic. Numerical results are presented to evaluate the accuracy of these approximations and their use in testing for randomness.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s11009-009-9156-0</doi><tpages>17</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1387-5841 |
| ispartof | Methodology and computing in applied probability, 2010-12, Vol.12 (4), p.731-747 |
| issn | 1387-5841 1573-7713 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_861546957 |
| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Accuracy Approximation Business and Management Computation Economics Electrical Engineering Life Sciences Mathematical models Mathematics and Statistics Methodology Position (location) Probability Randomness Statistics Studies |
| title | Approximations for a Three Dimensional Scan Statistic |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-19T13%3A31%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Approximations%20for%20a%20Three%20Dimensional%20Scan%20Statistic&rft.jtitle=Methodology%20and%20computing%20in%20applied%20probability&rft.au=Glaz,%20Joseph&rft.date=2010-12-01&rft.volume=12&rft.issue=4&rft.spage=731&rft.epage=747&rft.pages=731-747&rft.issn=1387-5841&rft.eissn=1573-7713&rft_id=info:doi/10.1007/s11009-009-9156-0&rft_dat=%3Cproquest_cross%3E2155165781%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=756679729&rft_id=info:pmid/&rfr_iscdi=true |