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Testing a tolerance hypothesis by means of an information distance
Applications of Mathematics, Tome 35 (1990) no. 6, pp. 458-470
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In the paper a test of the hypothesis $\mu+c \sigma \leq M$, $\mu - c \sigma \geq m$ on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
In the paper a test of the hypothesis $\mu+c \sigma \leq M$, $\mu - c \sigma \geq m$ on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
DOI : 10.21136/AM.1990.104428
Classification : 62E20, 62F03, 62F05
Keywords: hypothesis testing; Fisher information matrix; concentration of the statistical population in prescribed tolerance limits; statistical quality control; normal distribution; explicit formulas for critical regions; finite sample sizes; fourth moment 
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Rublík, František. Testing a tolerance hypothesis by means of an information distance. Applications of Mathematics, Tome 35 (1990) no. 6, pp. 458-470. doi: 10.21136/AM.1990.104428

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