Nonparametric Estimation in Renewal Theory I: The Empirical Renewal Function
نویسندگان
چکیده
منابع مشابه
Nonparametric Renewal Function Estimation and Smoothing by Empirical Data
We consider an estimate of the renewal function (rf) using a limited number of independent observations of the interarrival times for an unknown interarrival-time distribution (itd). The nonparametric estimate is derived from the rf-representation as series of distribution functions (dfs) of consecutive arrival times using a finite summation and approximations of the latter by empirical dfs. Du...
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In reliability or medical studies, we may only observe each ongoing renewal process for a certain period of time. When the underlying distribution F is arithmetic, Vardi (Ann. Statist. 10 (1982b), 772-785) developed the RT algorithm for nonparametric estimation. In this paper we extend the study to the nonarithmetic case and show that the choice of an arbitrary constant in the RT algorithm can ...
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(1) Sn = S0 + n ∑ i=1 Xi When S0 = 0 the renewal process is an ordinary renewal process; when S0 is a nonnegative random variable the renewal process is a delayed renewal process. In either case, the individual terms Sn of this sequence are called renewals, or sometimes occurrences. With each renewal process is associated a renewal counting process N (t ) that tracks the total number of renewal...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1993
ISSN: 0090-5364
DOI: 10.1214/aos/1176349266