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On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution
This article considers three related aspects of maximum likelihood estimation of parameters in the two-parameter Burr XII distribution. Specifically, we first provide further clarification to some limiting results in Wingo ( 1993 ). We then focus on details in a proof of the uniqueness of the maximu...
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| Published in: | Communications in statistics. Theory and methods 2009-01, Vol.38 (11), p.1916-1926 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c408t-697ef633125c20b1121e3100b3db85cd01973dcb11301ed445568ee8081a109c3 |
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| cites | cdi_FETCH-LOGICAL-c408t-697ef633125c20b1121e3100b3db85cd01973dcb11301ed445568ee8081a109c3 |
| container_end_page | 1926 |
| container_issue | 11 |
| container_start_page | 1916 |
| container_title | Communications in statistics. Theory and methods |
| container_volume | 38 |
| creator | Jalali, Assad Watkins, Alan J. |
| description | This article considers three related aspects of maximum likelihood estimation of parameters in the two-parameter Burr XII distribution. Specifically, we first provide further clarification to some limiting results in Wingo (
1993
). We then focus on details in a proof of the uniqueness of the maximum likelihood estimators. Finally, we consider using the likelihood approach for data which does not satisfy Wingo's criterion, and show that this results in fitting either a Pareto distribution or an intuitively sensible degenerate distribution to the data. The discussion here is completely general, and not restricted to data obtained under Type II censoring. |
| doi_str_mv | 10.1080/03610920802491758 |
| format | article |
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1993
). We then focus on details in a proof of the uniqueness of the maximum likelihood estimators. Finally, we consider using the likelihood approach for data which does not satisfy Wingo's criterion, and show that this results in fitting either a Pareto distribution or an intuitively sensible degenerate distribution to the data. The discussion here is completely general, and not restricted to data obtained under Type II censoring.</description><identifier>ISSN: 0361-0926</identifier><identifier>EISSN: 1532-415X</identifier><identifier>DOI: 10.1080/03610920802491758</identifier><identifier>CODEN: CSTMDC</identifier><language>eng</language><publisher>Philadelphia, PA: Taylor & Francis Group</publisher><subject>Burr XII ; Censored data ; Convex function ; Distribution theory ; Exact sciences and technology ; General topics ; Mathematics ; Maximum likelihood estimation ; Nonparametric inference ; Primary 62F10 ; Probability and statistics ; Probability theory and stochastic processes ; Profile likelihood ; Sciences and techniques of general use ; Secondary 62N02 ; Statistics</subject><ispartof>Communications in statistics. Theory and methods, 2009-01, Vol.38 (11), p.1916-1926</ispartof><rights>Copyright Taylor & Francis Group, LLC 2009</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c408t-697ef633125c20b1121e3100b3db85cd01973dcb11301ed445568ee8081a109c3</citedby><cites>FETCH-LOGICAL-c408t-697ef633125c20b1121e3100b3db85cd01973dcb11301ed445568ee8081a109c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=21777659$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Jalali, Assad</creatorcontrib><creatorcontrib>Watkins, Alan J.</creatorcontrib><title>On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution</title><title>Communications in statistics. Theory and methods</title><description>This article considers three related aspects of maximum likelihood estimation of parameters in the two-parameter Burr XII distribution. Specifically, we first provide further clarification to some limiting results in Wingo (
1993
). We then focus on details in a proof of the uniqueness of the maximum likelihood estimators. Finally, we consider using the likelihood approach for data which does not satisfy Wingo's criterion, and show that this results in fitting either a Pareto distribution or an intuitively sensible degenerate distribution to the data. The discussion here is completely general, and not restricted to data obtained under Type II censoring.</description><subject>Burr XII</subject><subject>Censored data</subject><subject>Convex function</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Nonparametric inference</subject><subject>Primary 62F10</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Profile likelihood</subject><subject>Sciences and techniques of general use</subject><subject>Secondary 62N02</subject><subject>Statistics</subject><issn>0361-0926</issn><issn>1532-415X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqFkEFLwzAYhoMoOKc_wFsu4qmar2maFrzonDqYzMOE3UqWpizaNjNJ2fbvzdj0MtBTPvie5wvvi9AlkBsgGbklNAWSx2GMkxw4y45QDxiNowTY7Bj1tvsoAOkpOnPugxBgPKM9NJ60-FWsddM1eKw_Va0XxpR46LxuhNemxZWx2C8Unq4MfhNWNMorix86a_FsNMKP2nmr592WPUcnlaiduti_ffT-NJwOXqLx5Hk0uB9HMiGZj9KcqyqlFGImYzIHiEFRIGROy3nGZEkg57SUYUEJqDJJGEszpTKSgQghJe2j693dpTVfnXK-aLSTqq5Fq0znCp5QTnIeAvYR7EhpjXNWVcXShmB2UwAptsUVB8UF52p_XTgp6sqKVmr3K8bAOU9ZHri7Hafb0FEjVsbWZeHFpjb2R6J_fcP_1Q-swq89_QZp-ZDW</recordid><startdate>20090101</startdate><enddate>20090101</enddate><creator>Jalali, Assad</creator><creator>Watkins, Alan J.</creator><general>Taylor & Francis Group</general><general>Taylor & Francis</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>20090101</creationdate><title>On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution</title><author>Jalali, Assad ; Watkins, Alan J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c408t-697ef633125c20b1121e3100b3db85cd01973dcb11301ed445568ee8081a109c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Burr XII</topic><topic>Censored data</topic><topic>Convex function</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Nonparametric inference</topic><topic>Primary 62F10</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Profile likelihood</topic><topic>Sciences and techniques of general use</topic><topic>Secondary 62N02</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jalali, Assad</creatorcontrib><creatorcontrib>Watkins, Alan J.</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>Communications in statistics. Theory and methods</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Jalali, Assad</au><au>Watkins, Alan J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution</atitle><jtitle>Communications in statistics. Theory and methods</jtitle><date>2009-01-01</date><risdate>2009</risdate><volume>38</volume><issue>11</issue><spage>1916</spage><epage>1926</epage><pages>1916-1926</pages><issn>0361-0926</issn><eissn>1532-415X</eissn><coden>CSTMDC</coden><abstract>This article considers three related aspects of maximum likelihood estimation of parameters in the two-parameter Burr XII distribution. Specifically, we first provide further clarification to some limiting results in Wingo (
1993
). We then focus on details in a proof of the uniqueness of the maximum likelihood estimators. Finally, we consider using the likelihood approach for data which does not satisfy Wingo's criterion, and show that this results in fitting either a Pareto distribution or an intuitively sensible degenerate distribution to the data. The discussion here is completely general, and not restricted to data obtained under Type II censoring.</abstract><cop>Philadelphia, PA</cop><pub>Taylor & Francis Group</pub><doi>10.1080/03610920802491758</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0361-0926 |
| ispartof | Communications in statistics. Theory and methods, 2009-01, Vol.38 (11), p.1916-1926 |
| issn | 0361-0926 1532-415X |
| language | eng |
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| source | Taylor and Francis:Jisc Collections:Taylor and Francis Read and Publish Agreement 2024-2025:Science and Technology Collection (Reading list) |
| subjects | Burr XII Censored data Convex function Distribution theory Exact sciences and technology General topics Mathematics Maximum likelihood estimation Nonparametric inference Primary 62F10 Probability and statistics Probability theory and stochastic processes Profile likelihood Sciences and techniques of general use Secondary 62N02 Statistics |
| title | On Maximum Likelihood Estimation for the Two Parameter Burr XII Distribution |
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