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Smooth nonparametric estimation of the distribution and density functions from record-breaking data. (English) Zbl 0825.62160
Summary: In some experiments, such as destructive stress testing and industrial quality control experiments, only values smaller than all previous ones are observed. Here, for such record-breaking data, kernel estimation of the cumulative distribution function and smooth density estimation is considered. For a single record-breaking sample, consistent estimation is not possible, and replication is required for global results. For \(m\) independent record-breaking samples, the proposed distribution function and density estimators are shown to be strongly consistent and asymptotically normal as \(m\rightarrow\infty\). Also, for small \(m\), the mean squared errors and biases of the estimators and their smoothing parameters are investigated through computer simulations.

MSC:
62-XX Statistics
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