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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 45, Fasc. 1,
pages 45 - 69
DOI: 10.37190/0208-4147.00217
Published online 30.6.2025
 

Unbiased estimation of exponential reliability for left censored data

Piotr Bolesław Nowak

Abstract:

The paper applies the Rao–Blackwell technique to construct an unbiased estimator of the reliability function in the exponential distribution under left censored data. The resulting estimator is a function of a sufficient statistic. However, we cannot conclude that it is a minimal variance estimator because the sufficient statistic is not complete. We also give an asymptotic confidence interval for reliability based on the estimator obtained. The performance of this estimator is compared to the maximum likelihood estimator via Monte Carlo simulation.

2010 AMS Mathematics Subject Classification: Primary 62N01; Secondary 62F12.

Keywords and phrases: exponential distribution, reliability function, unbiased estimation.

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