@article {IOPORT.04126492,
    author       = {Winter, B.B. and F\"oldes, A.},
    title        = {A product-limit estimator for use with length-biased data.},
    year         = {1988},
    journal      = {The Canadian Journal of Statistics},
    volume       = {16},
    number       = {4},
    issn         = {0319-5724},
    pages        = {337-355},
    publisher    = {Wiley-Blackwell for Statistical Society of Canada, Ottawa, ON},
    doi          = {10.2307/3314932},
    abstract     = {Authors' abstract: The following life-testing situation is considered. At some time in the distant past, n objects, from a population with life distribution F, were put in use; whenever an object failed, it was promptly replaced. At some time $\tau$, long after the start of the process, a statistician starts observing the n objects in use at that time; he knows the age of each of those n objects, and observes each of them for a fixed length of time $T\le \infty$, or until failure, whichever occurs first. In the case where T is finite, some of the observations may be censored; in the case where $T=\infty$, there is no censoring. The total life of an object in use at time $\tau$ is a length- biased observation from F. A nonparametric estimator of the (cumulative) hazard function is proposed, and is used to construct an estimator of F which is of the product-limit type. Strong uniform consistency results (for $n\to \infty)$ are obtained. An ``Aalen-Johansen'' identity, satisfied by any pair of life distributions and their (cumulative) hazard function, is used for obtaining rate of convergence results.},
    reviewer     = {P.Gaenssler},
    identifier   = {04126492},
}