Geodesic
Estimates of reliability for the normal distribution
Applications of Mathematics, Tome 25 (1980) no. 6, pp. 432-444.

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The minimum variance unbiased, the maximum likelihood, the Bayes, and the naive estimates of the reliability function of a normal distribution are studied. Their asymptotic normality is proved and asymptotic expansions for both the expectation and the mean squared error are derived. The estimates are then compared using the concept of deficiency. In the end an extensive Monte Carlo study of the estimates in small samples is given.
DOI : 10.21136/AM.1980.103882
Classification : 62F10, 62F12, 62F15, 62N05, 65C05
Keywords: estimates of reliability; normal distribution; minimum variance unbiased; maximum likelihood; reliability function 
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     title = {Estimates of reliability for the normal distribution},
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Hurt, Jan. Estimates of reliability for the normal distribution. Applications of Mathematics, Tome 25 (1980) no. 6, pp. 432-444. doi : 10.21136/AM.1980.103882. http://geodesic.mathdoc.fr/articles/10.21136/AM.1980.103882/

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