zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An urn model in the simulation of interval censored failure time data. (English) Zbl 0951.62087
Summary: A self-consistent algorithm was proposed by {\it B.W. Turnbull} [J. Am. Stat. Assoc. 69, 169-173 (1974; Zbl 0281.62044)] to estimate the distribution of $X$ on the basis of interval censored data of $X$. An interval censored $X$ means that $X$ is known either to lie inside an interval $(X_L,X_R]$, or to lie below $X_L$ or above $X_R$. The calculation of the estimates is not an easy task. In this article, an urn model is constructed to sample the random intervals and to calculate relevant probabilities. It is proved that using the interval data obtained from the urn model, consistent estimates can be obtained by using the self-consistency algorithm. A simulation example is provided to illustrate the procedure.

62N05Reliability and life testing (survival analysis)
65C60Computational problems in statistics
62N99Survival analysis and censored data
Full Text: DOI
[1] Cox, D.R., Oakes, D., 1984. Analysis of Survival Data. Chapman & Hall, New York.
[2] De Gruttola, V.; Lagakos, S. W.: Analysis of doubly-censored survival data, with application to AIDS.. Biometrics. 45, 1-11 (1989) · Zbl 0715.62223
[3] Finkelstein, D. M.: A proportional hazards model for interval-censored failure time data.. Biometrics. 42, 845-854 (1986) · Zbl 0618.62097
[4] Finkelstein, D. M.; Wolfe, R. A.: A semiparametric model for regression analysis of interval-censored failure time data.. Biometrics. 41, 933-945 (1985) · Zbl 0655.62101
[5] Gomez, G.; Lagakos, S. W.: Estimation of the infection time and latency distribution of AIDS with doubly censored data.. Biometrics. 50, 204-212 (1994) · Zbl 0826.62088
[6] Lawless, J.F., 1982. Statistical Models and Methods for Lifetime Data. Wiley, New York. · Zbl 0541.62081
[7] Leiderman, P. H.; Babu, D.; Kagia, J.; Kraemer, H. C.; Leiderman, G. H.: African infant precocity and some social influence during the first year.. Nature. 242, 247-249 (1973)
[8] Sun, J.: A non-parametric test for interval-censored failure time data with application to AIDS studies.. Statist. med. 15, 1387-1395 (1996)
[9] Turnbull, B. W.: Nonparametric estimation of a surviorship function with doubly censored data.. J. amer. Statist. assoc. 69, 169-173 (1974) · Zbl 0281.62044