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 : 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 definition the symbols ...
... 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 definition the symbols ...
Page 405
... is known ( Exercise 9.3 ) that C = { ( x1 , x2 ) : 9.5 ≤ x1 + x2 < ∞ } is a best critical region Ho of size 0.05 for testing the simple hypothesis H Sec . 9.2 ] Uniformly Most Powerful Tests 405 Uniformly Most Powerful Tests.
... is known ( Exercise 9.3 ) that C = { ( x1 , x2 ) : 9.5 ≤ x1 + x2 < ∞ } is a best critical region Ho of size 0.05 for testing the simple hypothesis H Sec . 9.2 ] Uniformly Most Powerful Tests 405 Uniformly Most Powerful Tests.
Page 412
... Ho : 00 ' , where 0 ' is a fixed positive H1 = number , and H1 : 00 ' , show that there is no uniformly most powerful test for testing Ho against H1 . 9.17 . Let X1 , X2 , ... , X25 denote a random sample of size 25 from a normal ...
... Ho : 00 ' , where 0 ' is a fixed positive H1 = number , and H1 : 00 ' , show that there is no uniformly most powerful test for testing Ho against H1 . 9.17 . Let X1 , X2 , ... , X25 denote a random sample of size 25 from a normal ...
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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. 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