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Estimating a survival curve when new is better than used in expectation
Author(s) -
Whitaker Lyn R.,
Samaniego Francisco J.
Publication year - 1989
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198910)36:5<693::aid-nav3220360513>3.0.co;2-f
Subject(s) - mathematics , estimator , random variable , consistency (knowledge bases) , distribution function , combinatorics , distribution (mathematics) , statistics , asymptotic distribution , empirical distribution function , discrete mathematics , mathematical analysis , physics , quantum mechanics
Let X be a positive random variable. The distribution F of X is said to be “new better than used in expectation,” or “NBUE,” if E(X) ⩾ E ( X – t | X > t) for all t ⩾ 0. Suppose X 1 , …, X n , is a random sample from an NBUE distribution F . The problem of estimating F by a distribution which is itself NBUE is considered. The estimator G n , defined as the NBUE distribution supported on the sample which minimizes the (sup norm) distance between the NBUE class and the empirical distribution function, is studied. The strong uniform consistency of G n , is proven, and a numerical algorithm for obtaining G n , is given. Our approach is applied to provide an estimate of the distribution of lifetime following the diagnosis of chronic granulocytic leukemia based on data from a National Cancer Institute study.