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 398
... number . Let C be a subset of the sample space such that : L ( 0 ; ... , X1 , X2 , . . . , Xn ) L ( 0 " ; X1 , X2 , ... 9 Xn ) L ( 0 ' ; X1 , X2 , xn ) ... ( a ) ( b ) L ( 0 " ; X1 , X2 , ( c ) α = Pr [ ( X1 , X2 , 9 2 , .. Xn ) < k ...
... number . Let C be a subset of the sample space such that : L ( 0 ; ... , X1 , X2 , . . . , Xn ) L ( 0 " ; X1 , X2 , ... 9 Xn ) L ( 0 ' ; X1 , X2 , xn ) ... ( a ) ( b ) L ( 0 " ; X1 , X2 , ( c ) α = Pr [ ( X1 , X2 , 9 2 , .. Xn ) < k ...
Page 410
... statistic Y = EX1 . We can generalize Example 5 by noting the following . Suppose that the random sample X1 , X2 , . . . , X , arises from a p.d.f. representing a regular case of the exponential class , namely ... Statistical Tests [ Ch . 9.
... statistic Y = EX1 . We can generalize Example 5 by noting the following . Suppose that the random sample X1 , X2 , . . . , X , arises from a p.d.f. representing a regular case of the exponential class , namely ... Statistical Tests [ Ch . 9.
Page 514
... statistic , we let c1 = C2 = = Сп 1 , show that we obtain a statistic equivalent to that used in the sign test ... 9 , compute the mean and the variance of this W .. 11.25 . If c , = 2 ' , i = 1 , 2 , . . . , n , the corresponding ...
... statistic , we let c1 = C2 = = Сп 1 , show that we obtain a statistic equivalent to that used in the sign test ... 9 , compute the mean and the variance of this W .. 11.25 . If c , = 2 ' , i = 1 , 2 , . . . , n , the corresponding ...
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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