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Keywords:
estimates of reliability; normal distribution; minimum variance unbiased; maximum likelihood; reliability function
estimates of reliability; normal distribution; minimum variance unbiased; maximum likelihood; reliability function
Summary:
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.
References:
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[2] J. Hurt: On estimation of reliability in the exponential case. Apl. Mat. 21 (1976), 263 - 272. MR 0468078 | Zbl 0354.62079
[3] J. Hurt: Asymptotic expansions of functions of statistics. Apl. Mat. 21 (1976), 444 - 456. MR 0418309 | Zbl 0354.62034
[4] A. N. Kolmogorov: Несмещенные оценки. AN SSSR, Ser. mat. 14 (1950), 303. MR 0036479 | Zbl 0052.36804
[5] C. R. Rao: Linear statistical inference and its applications. 2nd ed., Wiley, New York 1973. MR 0346957 | Zbl 0256.62002
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