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On the two-sided quality control
Applications of Mathematics, Tome 27 (1982) no. 2, pp. 87-95
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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 $\mu+c\sigma\leq m + \delta, \mu-c\sigma\geq m-\delta$, 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.
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 $\mu+c\sigma\leq m + \delta, \mu-c\sigma\geq m-\delta$, 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.
DOI : 10.21136/AM.1982.103950
Classification : 62E20, 62F03, 62N10, 62P30
Keywords: maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population 
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Rublík, František. On the two-sided quality control. Applications of Mathematics, Tome 27 (1982) no. 2, pp. 87-95. doi: 10.21136/AM.1982.103950

[1] H. Chernoff: On the distribution of the likelihood ratio. Ann. Math. Stat., 25, 1954, 573 - 578. | DOI | MR | Zbl

[2] H. Chernoff: Large-sample theory: parametric case. Ann. Math. Stat., 27, 1956, 1 - 22. | DOI | MR | Zbl

[3] D. J. Cowden: Statistical Methods in Quality Control. Englewood Cliffs, Prentice Hall 1957.

[4] H. Crarner: Mathematical Methods of Statistics. Princeton, Princelon University Press 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. | MR

[6] P. L. Feder: On the distribution of the log likelihood ratio test statistic when the true parameter is "near" the boundaries of the hypothesis regions. Ann. Math. Stat., 39, 1968, 2044 to 2055. | DOI | MR | Zbl

[7] L. Schmetterer: Introduction to Mathematical Statistics. Berlin, Springer - Verlag 1974. | MR | Zbl

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