On the two-sided quality control

František Rublík

Aplikace matematiky (1982)

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

Abstract

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Let the random variable X have the normal distribution N ( μ , σ 2 ) . Explicit formulas for maximum likelihood estimator of μ , σ are derived under the hypotheses μ + c σ m + δ , μ - c σ m - δ , where c , m , δ are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.

How to cite

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Rublík, 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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  1. H. Chernoff, 10.1214/aoms/1177728725, Ann. Math. Stat., 25, 1954, 573 - 578. (1954) Zbl0056.37102MR0065087DOI10.1214/aoms/1177728725
  2. H. Chernoff, 10.1214/aoms/1177728347, Ann. Math. Stat., 27, 1956, 1 - 22. (1956) Zbl0072.35703MR0076245DOI10.1214/aoms/1177728347
  3. D. J. Cowden, Statistical Methods in Quality Control, Englewood Cliffs, Prentice Hall 1957. (1957) 
  4. H. Crarner, Mathematical Methods of Statistics, Princeton, Princelon University Press 1966. (1966) 
  5. Ch. Eisenhart M. W. Hastay, W A. Wallis, Selected Techniques of Statistical Analysis for Scientific and Industrial Research and Production and Management Engineering, New York, McGraw-Hill 1947. (1947) MR0023505
  6. P. L. Feder, 10.1214/aoms/1177698032, Ann. Math. Stat., 39, 1968, 2044 to 2055. (1968) Zbl0212.23002DOI10.1214/aoms/1177698032
  7. L. Schmetterer, Introduction to Mathematical Statistics, Berlin, Springer - Verlag 1974. (1974) Zbl0295.62001MR0359100

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