## Nonparametric estimation from incomplete observations.(English)Zbl 0089.14801

Let $$P(t)$$ be the probability that an item from a given population will have lifetime exceeding $$t$$. For a sample of size $$N$$ let the observed times either to death or to other loss be $$t_1\leq t_2\leq t_3\leq \cdots\leq t_n$$. The maximum likelihood estimate of $$P(t)$$ is then $\widehat{P(t)}=\prod_r \frac{(N-r)}{(N-r+1)}$ where $$r$$ ranges over those integers for which $$t_r\leq t$$ and $$t_r$$ is a time to death. The mean and variance of $$\widehat{P(t)}$$ are computed. Comparisons of this estimate are made with reduced sample estimates and actuarial estimates.
Reviewer: D. R. Whitney

### MSC:

 62G05 Nonparametric estimation 62G08 Nonparametric regression and quantile regression

statistics
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