Estimates of reliability for the normal distribution

Jan Hurt

Aplikace matematiky (1980)

  • Volume: 25, Issue: 6, page 432-444
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hurt, Jan. "Estimates of reliability for the normal distribution." Aplikace matematiky 25.6 (1980): 432-444. <http://eudml.org/doc/15170>.

@article{Hurt1980,
abstract = {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.},
author = {Hurt, Jan},
journal = {Aplikace matematiky},
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},
language = {eng},
number = {6},
pages = {432-444},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimates of reliability for the normal distribution},
url = {http://eudml.org/doc/15170},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Hurt, Jan
TI - Estimates of reliability for the normal distribution
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 6
SP - 432
EP - 444
AB - 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.
LA - eng
KW - estimates of reliability; normal distribution; minimum variance unbiased; maximum likelihood; reliability function; estimates of reliability; normal distribution; minimum variance unbiased; maximum likelihood; reliability function
UR - http://eudml.org/doc/15170
ER -

References

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  1. J. L. Hodges, jr., E. L. Lehmann, 10.1214/aoms/1177696959, Ann. Math. Statist. 41 (1970), 783-801. (1970) Zbl0225.62063MR0272092DOI10.1214/aoms/1177696959
  2. J. Hurt, On estimation of reliability in the exponential case, Apl. Mat. 21 (1976), 263 - 272. (1976) Zbl0354.62079MR0468078
  3. J. Hurt, Asymptotic expansions of functions of statistics, Apl. Mat. 21 (1976), 444 - 456. (1976) Zbl0354.62034MR0418309
  4. A. N. Kolmogorov, Несмещенные оценки, AN SSSR, Ser. mat. 14 (1950), 303. (1950) Zbl0052.36804MR0036479
  5. C. R. Rao, Linear statistical inference and its applications, 2nd ed., Wiley, New York 1973. (1973) Zbl0256.62002MR0346957

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