In the first topic we describe a procedure that uses incomplete data to estimate failure rate and survival functions. Although the procedure is designed for discrete distributions, it applies in the continuous case also. / The procedure is based on the assumption of a piecewise constant failure rate. The resultant survival function estimator is a piecewise geometric function, denoted the Piecewise Geometric Estimator (PEGE). It is the discrete version of the piecewise exponential estimators proposed independently by Kitchin, Langberg and Proschan (1983) and Whittemore and Keller (1983), and it generalizes Umholtz's (1984) estimator designed for complete Exponential data. / The PEGE is attractive to users because it is computationally simple and realistic in that it decreases at every possible failure time: it therefore not only has the appearance of a survival function, but also provides realistic estimates of the failure rate function and the percentiles of the underlying distribution. The widely used Kaplan-Meier estimator (KME), being a step function, is not suited to estimating these quantities. / The PEGE is consistent and asymptotically normal under conditions more general than those of the standard model of random censorship. Although the PEGE and the KME are asymptotically equivalent, simulation studies show that in small samples the PEGE compares favourably with the KME in terms of efficiency but not in terms of bias. (Since the two estimators generally interlace, the PEGE's bias is not a disadvantage in practice). A variant of the PEGE is less biased than it and is even more efficient. The geometric percentile estimators perform better than do the Kaplan-Meier counterparts in terms of both bias and efficiency. A pilot study indicates that the small sample behaviour of bootstrap confidence interval procedures for both survival probabilities and percentiles is considerably improved when a geometric estimator is used instead of the KME. / In the second topic we study preservation of total positivity orderings under integration in general, and, more specifically, under convolution, mixing and the formation of coherent systems. / Source: Dissertation Abstracts International, Volume: 47-02, Section: B, page: 0689. / Thesis (Ph.D.)--The Florida State University, 1985.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75778 |
| Contributors | MIMMACK, GILLIAN MARY., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 154 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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