# Estimates of reliability for the normal distribution

Aplikace matematiky (1980)

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

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topHurt, 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

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

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