Let (PI)(,1), (PI)(,2), ..., (PI)(,k) be k exponential populations. The problem of the ranking and selection for these k populations is formulated in order to accommodate censored observations. The data under study are assumed to be generated from three types of censoring mechanisms--Type-I, Type-II and random censoring. / Let X(,i{1}) be the minimum order statistic in the sample of size n from the population (PI)(,i), i = 1, 2, ..., k. A selection procedure for selecting the largest location parameter, (lamda)(,{k}), under Type-I censoring is defined in terms of a set of minima Y(,i) = min(X(,i{1}), T), i = 1, 2, ..., k, where T is a fixed time. A procedure with respect to the largest location parameter under Type-II censoring is proposed based on X(,i{1}). These two procedures are shown to be asymptotically equivalent. / The ranking and selection for scale parameters based on Type-II censored data are investigated under two formulations, i.e., Bechhofer's indifference zone approach and Gupta's subset selection approach. The selection rule proposed under Gupta's formulation is the same as the procedure studied independently by Huang and Huang (1980, Proc. of Conference on Recent Developments in Statistical Methods and Applications. Academia Sinica, Taipei, Taiwan). It is noted that this procedure is equivalent to the procedure investigated by Gupta (1963, Ann. Inst. Statist. Math. 14, 199-216) for gamma populations with the complete data. / The scale parameter problem, subjected to Type-I censoring, is also examined. We introduce the idea of using the total time on test (TTOT) statistic as the selection statistic. The exact distribution of the TTOT statistic is found and several properties of the section rule proposed for Type-I censored data are discussed. / Finally, the selection problem under random censorship is studied. The maximum likelihood estimate (MLE) T(,i) of the scale parameter (theta)(,i) is obtained from the randomly censored data. A selection procedure is proposed based on T(,i), i = 1, 2, ..., k. Under certain conditions we show that Gupta's (1963) constants can be used in the rule proposed under the random censoring model. The bound on P* probability below which the procedure is well-defined is given. / Source: Dissertation Abstracts International, Volume: 43-07, Section: B, page: 2260. / Thesis (Ph.D.)--The Florida State University, 1982.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74900 |
| Contributors | KIM, JEE SOO., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 150 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
Page generated in 0.0017 seconds