Introduction to Mathematical Statistics |
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Page 182
... ratio tests . " A likelihood ratio test , as just remarked , is not necessarily a most powerful test , but it has been proved in the literature that such a test often has desirable properties A certain terminology and notation will be ...
... ratio tests . " A likelihood ratio test , as just remarked , is not necessarily a most powerful test , but it has been proved in the literature that such a test often has desirable properties A certain terminology and notation will be ...
Page 183
... ratio of L ( w ) to L ( 2 ) could not provide a basis for a test of Ho against H1 . Suppose , however , we modify this ratio in the following manner : We shall find the maximum of L ( w ) in w ; that is , the maximum of L ( w ) with ...
... ratio of L ( w ) to L ( 2 ) could not provide a basis for a test of Ho against H1 . Suppose , however , we modify this ratio in the following manner : We shall find the maximum of L ( w ) in w ; that is , the maximum of L ( w ) with ...
Page 189
... ratio principle leads to the same test , when testing a null simple hypothesis Ho against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there are only two points in 2 . n 9.24 . Verify ...
... ratio principle leads to the same test , when testing a null simple hypothesis Ho against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there are only two points in 2 . n 9.24 . Verify ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
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Common terms and phrases
A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²