Let F be a life distribution with survival function F(' )(TBOND)(' )1 - F. Conditional on survival to time t, the remaining life has survival function / F(,t)(x) = F(t + x)/F(t), x (GREATERTHEQ) 0, 0 (LESSTHEQ) t < F('-1)(1). / The mean residual life function of F is / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / if F has a finite mean. The (alpha)-percentile or quantile (0 < (alpha) < 1) residual life function of F is / q(,(alpha),F)(t) = F(,t)('-1)((alpha)) = F('-1)(1 - (alpha)F(t)) - t, 0 (LESSTHEQ) t < F('-1)(1), / where (alpha) = 1 - (alpha). Statisticians find it useful to categorize life distributions according to different aging properties. Categories which involve m(,F)(t) are the decreasing mean residual life (DMRL) class and the new better than used in expectation (NBUE) class. The DMRL class consists of distributions F such that m(,F)(t) is monotone decreasing on (0, F('-1)(1)) and the NBUE class consists of distributions F such that m(,F)(0) (GREATERTHEQ) m(,F)(t) for all 0 < t < F('-1)(1). Analogous categories which involve q(,(alpha),F)(t) are the decreasing (alpha)-percentile residual life (DPRL-(alpha)) class and the new better than used with respect to the (alpha)-percentile (NBUP-(alpha)) class. / The mean residual life function is of interest in biometry, actuarial studies and reliability, and the DMRL and NBUE classes of life distributions are useful for modelling situations where items deteriorate with age. In the statistical literature, there are several papers which consider properties or estimation of the mean residual life function or consider testing situations involving the DMRL and NBUE classes. Only one previous paper discusses the (alpha)-percentile residual life function. This dissertation is concerned with properties and estimation of the (alpha)-percentile residual life function, and with testing problems involving the (alpha)-percentile residual life function. / Properties of q(,(alpha),F)(t) and of the DPRL-(alpha), NBUP-(alpha) and their dual classes are studied in Chapter II. In Chapter III, tests are developed for testing exponentiality against alternatives of DPRL-(alpha) and NBUP-(alpha). In Chapter IV, these tests are extended to accommodate randomly censored data. In Chapter V, a distribution-free two-sample test is developed for testing the hypothesis that two life distributions F and G are equal against the alternative that q(,(alpha),F)(t) (GREATERTHEQ) q(,(alpha),G)(t) for all t. In Chapter VI, strong consistency, asymptotic normality, bias and mean squared error of the estimator F(,n)('-1)(1(' )-(' )(alpha)F(,n)(t)) - t of q(,(alpha),F)(t) are studied, where F(,n) is the empirical distribution function and F(,n)(' )(TBOND)(' )1 - F(,n). / Source: Dissertation Abstracts International, Volume: 43-02, Section: B, page: 0467. / Thesis (Ph.D.)--The Florida State University, 1982.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74771 |
| Contributors | JOE, HARRY SUE WAH., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 152 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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