# On the two-sided quality control

Aplikace matematiky (1982)

- Volume: 27, Issue: 2, page 87-95
- ISSN: 0862-7940

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topRublík, František. "On the two-sided quality control." Aplikace matematiky 27.2 (1982): 87-95. <http://eudml.org/doc/15228>.

@article{Rublík1982,

abstract = {Let the random variable $X$ have the normal distribution $N(\mu ,\sigma ^2)$. Explicit formulas for maximum likelihood estimator of $\mu ,\sigma $ are derived under the hypotheses $\mu +c\sigma \le m + \delta , \mu -c\sigma \ge m-\delta $, where $c,m,\delta $ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.},

author = {Rublík, František},

journal = {Aplikace matematiky},

keywords = {maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population; maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population},

language = {eng},

number = {2},

pages = {87-95},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the two-sided quality control},

url = {http://eudml.org/doc/15228},

volume = {27},

year = {1982},

}

TY - JOUR

AU - Rublík, František

TI - On the two-sided quality control

JO - Aplikace matematiky

PY - 1982

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 27

IS - 2

SP - 87

EP - 95

AB - Let the random variable $X$ have the normal distribution $N(\mu ,\sigma ^2)$. Explicit formulas for maximum likelihood estimator of $\mu ,\sigma $ are derived under the hypotheses $\mu +c\sigma \le m + \delta , \mu -c\sigma \ge m-\delta $, where $c,m,\delta $ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.

LA - eng

KW - maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population; maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population

UR - http://eudml.org/doc/15228

ER -

## References

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- H. Chernoff, 10.1214/aoms/1177728347, Ann. Math. Stat., 27, 1956, 1 - 22. (1956) Zbl0072.35703MR0076245DOI10.1214/aoms/1177728347
- D. J. Cowden, Statistical Methods in Quality Control, Englewood Cliffs, Prentice Hall 1957. (1957)
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- P. L. Feder, 10.1214/aoms/1177698032, Ann. Math. Stat., 39, 1968, 2044 to 2055. (1968) Zbl0212.23002MR0234553DOI10.1214/aoms/1177698032
- L. Schmetterer, Introduction to Mathematical Statistics, Berlin, Springer - Verlag 1974. (1974) Zbl0295.62001MR0359100

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