Given that an item is of age t, the expected value of the random remaining life is called the mean residual life (MRL) at age t. We propose two new nonparametric classes of life distributions for modeling aging based on MRL. The first class of life distributions consists of those with "increasing initially, then decreasing mean residual life" (IDMRL). The IDMRL class models aging that is initially beneficial, then adverse. The second class, "decreasing, then increasing mean residual life" (DIMRL), models aging that is initially adverse, then beneficial. We present situations where IDMRL (DIMRL) distributions are useful models. We propose two testing procedures for H(,0): constant MRL (i.e., exponentiality) versus H(,1): IDMRL, but not constant MRL (or H(,1)(''): DIMRL, but not constant MRL). The first testing procedure assumes the turning point, (tau), from IMRL to DMRL is specified by the user or is known. Our IDMRL((tau)) test statistic, T(,n), is a differentiable statistical function of order 1; thus, T(,n), suitably standardized is asymptotically normal. The second procedure assumes knowledge of the proportion, (rho), of the population that "dies" at or before the turning point (knowledge of (tau) itself is not assumed). We use L-statistic theory to show our IDMRL((rho)) test statistic, V(,n)('*), appropriately standardized is asymptotically normal. The exact null distribution of V(,n)('*) is established. For each of these procedures an application is given. After this we modify the complete data tests to yield analogous censored data procedures. The standard Kaplan-Meier Estimator is a key tool that we exploit for our censored data tests. A limited Monte Carlo study investigates the censored data procedures. / Source: Dissertation Abstracts International, Volume: 45-09, Section: B, page: 2979. / Thesis (Ph.D.)--The Florida State University, 1984.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75428 |
| Contributors | GUESS, FRANK MITCHELL., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 103 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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