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On estimation of hazard function. (English) Zbl 0597.62027

Summary: We consider two estimates of the hazard function (or the failure rate \(h(x)=f(x)/(1-F(x))\) where f and F are the density and distribution functions. Estimates are based on certain smoothed estimates of f(x). We establish almost sure uniform convergence (in x) of these estimates and give rates of almost sure uniform convergence. Extension to the multivariate case is also considered.

MSC:

62G05 Nonparametric estimation
62N05 Reliability and life testing
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