Related Experiment Video
Updated: Jul 17, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
Published on: June 3, 2009
Smooth estimation of the reliability function
K B Kulasekera1, C L Williams, M Coffin
1Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-1907, USA.
Abstract:
Problems with censored data arise quite frequently in reliability applications. Estimation of the reliability function is usually of concern. Reliability function estimators proposed by Kaplan and Meier (1958), Breslow (1972), are generally used when dealing with censored data. These estimators have the known properties of being asymptotically unbiased, uniformly strongly consistent, and weakly convergent to the same Gaussian process, when properly normalized. We study the properties of the smoothed Kaplan-Meier estimator with a suitable kernel function in this paper. The smooth estimator is compared with the Kaplan-Meier and Breslow estimators for large sample sizes giving an exact expression for an appropriately normalized difference of the mean square error (MSE) of the two estimators. This quantifies the deficiency of the Kaplan-Meier estimator in comparison to the smoothed version. We also obtain a non-asymptotic bound on an expected L1-type error under weak conditions. Some simulations are carried out to examine the performance of the suggested method.
Related Concept Videos
Confidence Intervals
A confidence...
Estimating Population Mean with Known Standard Deviation
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...
Confidence Interval for Estimating Population Mean
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
Estimating Population Standard Deviation
Expected Frequencies in Goodness-of-Fit Tests
Testing a Claim about Standard Deviation
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

