maximum likelihood statistic; tables of critical values; two-sided hypotheses; normal population
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.
 D. J. Cowden: Statistical Methods in Quality Control. Englewood Cliffs, Prentice Hall 1957.
 H. Crarner: Mathematical Methods of Statistics. Princeton, Princelon University Press 1966.
 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 0023505
 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 10.1214/aoms/1177698032
| MR 0234553
| Zbl 0212.23002
 L. Schmetterer: Introduction to Mathematical Statistics
. Berlin, Springer - Verlag 1974. MR 0359100
| Zbl 0295.62001