Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 397
... best critical region C of size a = for testing Ho against H ,. We note that Pr ( Xe A1 ; H1 ) = and that Pr ( Xe A1 ; H1 ) = 1024. Thus , if the set A , is used as a critical region of size α = 2 , we have the intolerable situation that ...
... best critical region C of size a = for testing Ho against H ,. We note that Pr ( Xe A1 ; H1 ) = and that Pr ( Xe A1 ; H1 ) = 1024. Thus , if the set A , is used as a critical region of size α = 2 , we have the intolerable situation that ...
Page 406
... critical region should be a best critical region for testing Ho against each simple hypothesis in H1 . That is , the power function of the test that corresponds to this critical region should be at least as great as the power function ...
... critical region should be a best critical region for testing Ho against each simple hypothesis in H1 . That is , the power function of the test that corresponds to this critical region should be at least as great as the power function ...
Page 408
... best critical region for testing Ho : 00 ' against the hypothesis 0 = 0 " provided that 0 " > 0 ' , while the second expression defines a best critical region for testing H1 : 00 ' against the hypothesis 0 = 0 " provided that 0 " < 0 ...
... best critical region for testing Ho : 00 ' against the hypothesis 0 = 0 " provided that 0 " > 0 ' , while the second expression defines a best critical region for testing H1 : 00 ' against the hypothesis 0 = 0 " provided that 0 " < 0 ...
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²