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Gulati, Sneh; Padgett, W. J.

Smooth nonparametric estimation of the hazard and hazard rate functions from record-breaking data. (English) Zbl 0803.62028

J. Stat. Plann. Inference 42, No. 3, 331-341 (1994).
Summary: Often in industrial quality control experiments and destructive stress testing, only values smaller than all previous ones are observed. Here, from such record-breaking data, non-parametric estimation of the hazard function and the hazard rate is considered. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence, replication is required and for \(m\) such independent record-breaking samples, strong consistency of the estimators is established as \(m\to \infty\). Also, the hazard function estimators are shown to be asymptotically normal. Finally, for small \(m\), the mean squared errors and biases of the estimators are examined through computer simulations.

Cited in 8 Documents

MSC:

62G05 Nonparametric estimation
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
62N05 Reliability and life testing
62P30 Applications of statistics in engineering and industry; control charts

Keywords:

kernel estimation; asymptotic normality; quality control; destructive stress testing; record-breaking data; hazard function; hazard rate; strong consistency; mean squared errors; biases; simulations
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References:

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