Sequential AnalysisPart I: General theory -- 1. Elements of the current theory of testing statistical hypotheses -- 2. Sequential test of a statistical hypothesis: general discussion -- 3. The sequential probability ratio test for testing a simple hypotheses H0 against a single alternative H1 -- 4. Outline of a theory of sequential tests of simple and composite hypotheses against a set of alternatives -- Part II: Application of the general theory to special cases -- 5. Testing the mean of a binomial distribution (acceptance inspection of a lot where each unit is classified into one of two categories) -- 6. Testing the difference between the means of two binomial distributions (double dichotomies) -- 7. Testing that the mean of a normal distribution with known standard deviation falls short of a given value -- 8. Testing that the standard deviation of a normal distribution does not exceed a given value -- 9. Testing that the mean of a normal distribution with known variance is equal to a specified value -- Part III: The problem of multi-valued decisions and estimation -- 10. The choice of a hypothesis from a set of mutually exclusive hypotheses (multi-valued decision) -- 11. The problem of sequential estimation. |
Contents
INTRODUCTION | 1 |
83 | 5 |
SEQUENTIAL TEST OF A STATISTICAL | 22 |
Copyright | |
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acceptance of H approximation ASN function binomial distribution characteristic function compute conditional expected value consider critical region defectives defined denote the probability derive equal equation example exceed expected number expected value f(xm finite number follows formula H₁ H₁ is true Hence hypothesis H inequalities L₁ mean non-defective normally distributed number of observations observations required obtain OC curve OC function optimum p₁ parameter point parameter space preassigned value preference for acceptance preference for rejection probability density function probability distribution probability ratio test random variable rejection number risk function Rm¹ sample x1 second kind Section sequential analysis sequential probability ratio sequential process sequential sampling plan sequential test simple hypothesis Statistical Suppose terminate test procedure testing the hypothesis tion u₁ unknown parameter upper bound weight functions wrong decision x₁ zone of indifference zone of preference α β Ро მი