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 396
... Ho . That is , the terms " test " and " critical region " can , in this sense , be used interchangeably . Thus , if we ... testing the simple hypothesis Ho against the alternative simple hypothesis H1 . In this definition the symbols Pr ...
... Ho . That is , the terms " test " and " critical region " can , in this sense , be used interchangeably . Thus , if we ... testing the simple hypothesis Ho against the alternative simple hypothesis H1 . In this definition the symbols Pr ...
Page 406
... test of a simple hypothesis Ho that is a best test of H。 against every simple hypothesis in the alternative composite hypothesis H1 . We now define a critical region , when it exists , which is a best critical region for testing a simple ...
... test of a simple hypothesis Ho that is a best test of H。 against every simple hypothesis in the alternative composite hypothesis H1 . We now define a critical region , when it exists , which is a best critical region for testing a simple ...
Page 412
... testing Ho against H1 . = 9.16 . If , in Example 2 of this section , H1 : 00 ' , where 0 ' is a fixed positive number , and H , : 00 ' , show that there is no uniformly most powerful test for testing Ho against H1 . 9.17 . Let X1 , X2 ...
... testing Ho against H1 . = 9.16 . If , in Example 2 of this section , H1 : 00 ' , where 0 ' is a fixed positive number , and H , : 00 ' , show that there is no uniformly most powerful test for testing Ho against H1 . 9.17 . Let X1 , X2 ...
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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