Introduction to Mathematical Statistics |
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Page 179
... accordance with Theorem 1 , has a uniform distribution on the interval ( 0 , 1 ) . Thus F ( X1 ) , F ( X2 ) ... accordance with Equation ( 1 ) , Section 6.1 , the joint p.d.f. of Z1 , Z2 , ... , Z , is given by Z 2 = n ' h ( Z1 , Z2 ...
... accordance with Theorem 1 , has a uniform distribution on the interval ( 0 , 1 ) . Thus F ( X1 ) , F ( X2 ) ... accordance with Equation ( 1 ) , Section 6.1 , the joint p.d.f. of Z1 , Z2 , ... , Z , is given by Z 2 = n ' h ( Z1 , Z2 ...
Page 258
... accordance with a prescribed test , leads to the rejection of the hypo- thesis under consideration . Then C is called the critical region of the test . Definition 4. The power function of a test of a statistical hypothesis H。 against ...
... accordance with a prescribed test , leads to the rejection of the hypo- thesis under consideration . Then C is called the critical region of the test . Definition 4. The power function of a test of a statistical hypothesis H。 against ...
Page 279
... accordance with the Neyman - Pearson theorem , a best test of H。 against H1 . ... ) n = We first investigate the decision function approach to the problem of testing a simple hypothesis against a simple alternative hypothesis . Let the ...
... accordance with the Neyman - Pearson theorem , a best test of H。 against H1 . ... ) n = We first investigate the decision function approach to the problem of testing a simple hypothesis against a simple alternative hypothesis . Let the ...
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Common terms and phrases
A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES F distribution function F(x given hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variables X₁ variance o² W₁ X₁ X₁ and X2 X₂ x²(n Y₂ Z₁ zero elsewhere μ₁ σ²