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 30
... defined for subsets C of % , whereas Px is defined for subsets A of A , and , in general , they are not the same set function . Nevertheless , they are closely related and some authors even drop the index X and write P ( A ) for Px ( A ) ...
... defined for subsets C of % , whereas Px is defined for subsets A of A , and , in general , they are not the same set function . Nevertheless , they are closely related and some authors even drop the index X and write P ( A ) for Px ( A ) ...
Page 110
... definition of a conditional p.d.f. If f ( x1 ) > 0 , the symbol f2 ... | 1 ( X2 , ... , xn | X , ) is defined by the relation f2 .... ( x2 , ... , X „ | X1 ) = ' 1 f ( x1 , x2 , ... , Xn ) fi ( x1 ) n 9 - and f2 .... ( X2 , ... , x | x1 ) ...
... definition of a conditional p.d.f. If f ( x1 ) > 0 , the symbol f2 ... | 1 ( X2 , ... , xn | X , ) is defined by the relation f2 .... ( x2 , ... , X „ | X1 ) = ' 1 f ( x1 , x2 , ... , Xn ) fi ( x1 ) n 9 - and f2 .... ( X2 , ... , x | x1 ) ...
Page 285
Robert V. Hogg, Allen Thornton Craig. Definition 6. The power function of a test of a statistical hypothesis H。 against an alternative hypothesis H , is that function , defined for all distributions under consideration , which yields ...
Robert V. Hogg, Allen Thornton Craig. Definition 6. The power function of a test of a statistical hypothesis H。 against an alternative hypothesis H , is that function , defined for all distributions under consideration , which yields ...
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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 g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ 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 sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²