Estimation of parameters in logistic and log-logistic distribution with grouped data
In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration...
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| Published in | Lifetime data analysis Vol. 13; no. 3; pp. 421 - 429 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Springer Nature B.V
01.09.2007
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1380-7870 1572-9249 |
| DOI | 10.1007/s10985-007-9038-0 |
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| Abstract | In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study. |
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| AbstractList | In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study. In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study.In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study. In many situations, instead of a complete sample, data are available only in grouped form. For example, grouped failure time data occur in studies in which subjects are monitored periodically to determine whether failure has occurred in the predetermined intervals. Here the model under consideration is the log-logistic distribution. This paper demonstrates the existence and uniqueness of the MLEs of the parameters of the logistic distribution under mild conditions with grouped data. The times with the maximum failure rate and the mode of the p.d.f. of the log-logistic distribution are also estimated based on the MLEs. The methodology is further studied with simulations and exemplified with a data set with artificially introduced grouping from a locomotive life test study. [PUBLICATION ABSTRACT] |
| Author | Guo, Shengru Zhou, Yan Yan Mi, Jie |
| Author_xml | – sequence: 1 givenname: Yan Yan surname: Zhou fullname: Zhou, Yan Yan – sequence: 2 givenname: Jie surname: Mi fullname: Mi, Jie – sequence: 3 givenname: Shengru surname: Guo fullname: Guo, Shengru |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/17546498$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1016/0022-1694(88)90015-7 10.1046/j.1600-0528.2003.00116.x 10.1002/(SICI)1521-4036(199907)41:4<431::AID-BIMJ431>3.0.CO;2-U 10.1214/aos/1176345516 10.1016/S0169-7161(01)20016-9 10.1002/(SICI)1097-0258(19990515)18:9<1111::AID-SIM102>3.0.CO;2-V |
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| DOI | 10.1007/s10985-007-9038-0 |
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| References | 9038_CR8 RC Gupta (9038_CR3) 1999; 41 MI Ahmad (9038_CR1) 1988; 98 R Leroy (9038_CR5) 2003; 31 A Oldehinkel (9038_CR7) 1999; 18 N Balakrishnan (9038_CR2) 2001; 20 T Makelanen (9038_CR6) 1981; 9 FJ Lawless (9038_CR4) 2003 14986914 - Community Dent Oral Epidemiol. 2003 Dec;31(6):463-70 10378259 - Stat Med. 1999 May 15;18(9):1111-8 |
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| SubjectTerms | Computer Simulation Data analysis Failure analysis Likelihood Functions Logistic Models Logistics Mathematical models Random variables Sample size Simulation Studies |
| Title | Estimation of parameters in logistic and log-logistic distribution with grouped data |
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