This research contributes to the theory and methods of testing hypotheses for classes of life distributions. Two classes of life distributions considered in this dissertation are: (1) The New Better Than Used (NBU) Class: The life distribution F is NBU if F(x+y)(' )(LESSTHEQ)(' )F(x)F(y) for all x, y (GREATERTHEQ) 0, where F(' )(TBOND)(' )1 - F. (2) The New Better Than Used at t(,0) (NBU-t(,0)) Class: The life distribution F is NBU-t(,0) if F(x+t(,0))(' )(LESSTHEQ)(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0. / The NBU and NBU-t(,0) classes have dual classes (New Worse Than Used and New Worse Than Used At t(,0), respectively) defined by reversing the inequality. / The NBU-t(,0) class is a new class of life distributions and contains the NBU class. We study the basic properties of the NBU-t(,0) class and propose a test of H(,0): F(x+t(,0))(' )=(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0, versus H(,A): F(x+t(,0))(' )(LESSTHEQ)(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0 and the inequality holds for some x (GREATERTHEQ) 0, based on a complete random sample X(,1), ..., X(,n) from F. Our test can also be used to test H(,0) against the NWU-t(,0) alternatives. Asymptotic relative efficiencies of our test with respect to the Hollander and Proschan (1972, Ann. Math. Statist. 43, 1136-1146) NBU test are calculated for several distributions. / We extend our test of H(,0) versus H(,A) to accommodate randomly censored data. For the censored data situation our test is based on the statistic / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where F is the Kaplan-Meier (1958, J. Amer. Statist. Assoc. 53, 457-481) estimator of(' )F. Under mild regularity conditions on the amount of censoring, a consistent test of H(,0) versus H(,A) for the randomly censored model is obtained. / In Chapter III we develop a two-sample NBU test of the null hypothesis that two distributions F and G are equal, versus the alternative that F is "more NBU" than is G. Our test is based on the statistic / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where m and n are the sample sizes from F and G, and F(,m) and G(,n) are the empirical distributions of F and G. Asymptotic normality of T(,m,n), suitably normalized, is a direct consequence of Hoeffding's (1948, Ann. Math. Statist. 19, 293-325) U-statistic theorem. Then, using a consistent estimator of the null asymptotic variance of N(' 1/2)T(,m,n), where N = m + n, we obtain an asymptotically distribution-free test. We extend the two-sample NBU test to the k-sample case. / Our test of H(,0) versus H(,A) utilizes the Kaplan-Meier estimator. However, there are other possible estimators of the survival function for the randomly censored model. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI / Source: Dissertation Abstracts International, Volume: 43-10, Section: B, page: 3290. / Thesis (Ph.D.)--The Florida State University, 1982.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74958 |
| Contributors | PARK, DONG HO., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 94 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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