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 H1 : 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 H1 : 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 396
... simple hypotheses Ho : 00 ' and H1 : 0 = 0 " . Thus Ω = { 0:00 ' , 0 " ) . We now define a best critical region ( and hence a best test ) for testing the simple hypothesis Ho against the alternative simple hypothesis H1 . In this ...
... simple hypotheses Ho : 00 ' and H1 : 0 = 0 " . Thus Ω = { 0:00 ' , 0 " ) . We now define a best critical region ( and hence a best test ) for testing the simple hypothesis Ho against the alternative simple hypothesis H1 . In this ...
Page 407
... simple hypothesis H1 : 0 = 0 ' against the simple hypothesis 0 = 0 " . It remains to determine c , so that this critical region has the desired size a . If H , is true , the random variable X ? / 0 ' has a chi - square distribution with ...
... simple hypothesis H1 : 0 = 0 ' against the simple hypothesis 0 = 0 " . It remains to determine c , so that this critical region has the desired size a . If H , is true , the random variable X ? / 0 ' has a chi - square distribution with ...
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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. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²