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
... 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 the ...
... 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 the ...
Page 406
... critical region , when it exists , which is a best critical region for testing a simple hypothesis Ho against an alternative composite hypothesis H ,. It seems desirable that this critical region should be a best critical region for ...
... critical region , when it exists , which is a best critical region for testing a simple hypothesis Ho against an alternative composite hypothesis H ,. It seems desirable that this critical region should be a best critical region for ...
Page 408
... 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 ...
... 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