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Bruce W. Turnbull, The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data, Journal of the Royal Statistical Society: Series B (Methodological), Volume 38, Issue 3, July 1976, Pages 290–295, https://doi.org/10.1111/j.2517-6161.1976.tb01597.x
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Summary
This paper is concerned with the non-parametric estimation of a distribution function F, when the data are incomplete due to grouping, censoring and/or truncation. Using the idea of self-consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. An application to hypothesis testing is indicated.
empirical distribution function, survival curve, censoring, truncation, grouping, maximum likelihood, kaplan–meier product limit estimator, self-consistency, newton–raphson, multinomial distribution, logrank test
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