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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.
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