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December, 1957 Transformation of the Fundamental Relationships in Sequential Analysis
H. Blasbalg
Ann. Math. Statist. 28(4): 1024-1028 (December, 1957). DOI: 10.1214/aoms/1177706805


For the class of distribution functions given by $$dP(x, \theta) = \exp \lbrack r(\theta)A(x) + s(\theta)B(x)\rbrack dw(x),$$ it is shown that a set of three transformations can be introduced which completely define the Sequential Probability Ratio Test for testing a hypothesis $H_0$ against $H_1$. When the observer specifies the threshold parameters $\theta_0$ and $\theta_1$ corresponding to the hypotheses $H_0$ and $H_1$ and the strength $\alpha, \beta$ of the test, he specifies the three transformations and hence the Sequential Test. However, there is an infinity of sets of parameter points $(\theta_0, \theta_1, \alpha, \beta)$ which satisfy the same transformations and hence define the same Sequential Test. The Operating Characteristic Function and the Average Sample Number Function are derived in terms of these transformations.


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H. Blasbalg. "Transformation of the Fundamental Relationships in Sequential Analysis." Ann. Math. Statist. 28 (4) 1024 - 1028, December, 1957.


Published: December, 1957
First available in Project Euclid: 27 April 2007

zbMATH: 0083.14804
MathSciNet: MR93882
Digital Object Identifier: 10.1214/aoms/1177706805

Rights: Copyright © 1957 Institute of Mathematical Statistics

Vol.28 • No. 4 • December, 1957
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