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 287
... simple hypothesis H。: 0 = 1 against the alternative simple hypothesis H1 : 02 , use a random sample X1 , X2 of size n = 2 and define the critical region to be C = { ( x1 , x2 ) ; } ≤ x , x2 } . Find the power function of the test ...
... simple hypothesis H。: 0 = 1 against the alternative simple hypothesis H1 : 02 , use a random sample X1 , X2 of size n = 2 and define the critical region to be C = { ( x1 , x2 ) ; } ≤ x , x2 } . Find the power function of the test ...
Page 402
... hypothesis H , be simple , namely that they completely specify the distributions . With this in mind , we see that the simple hypotheses H。 and H1 do not need to be hypotheses about the parameters of a distribution , nor , as a matter ...
... hypothesis H , be simple , namely that they completely specify the distributions . With this in mind , we see that the simple hypotheses H。 and H1 do not need to be hypotheses about the parameters of a distribution , nor , as a matter ...
Page 406
... simple hypothesis H1 : 02 against each simple hypothesis in the composite hypothesis H , : 0 > 2 . The preceding example affords an illustration of a test of a simple hypothesis Ho that is a best test of H。 against every simple ...
... simple hypothesis H1 : 02 against each simple hypothesis in the composite hypothesis H , : 0 > 2 . The preceding example affords an illustration of a test of a simple hypothesis Ho that is a best test of H。 against every simple ...
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Common terms and phrases
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