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. |
From inside the book
Results 1-3 of 15
Page 325
... 9 However , we find that y1 = w ( z ) or , equivalently , u1 ( x1 , x2 ,. Xn ) ... depend upon 0 , the factorization theorem implies that Z = u ( Y1 ) is also ... depend upon 0. We say this because every function Z = u ( Y1 ) with a single ...
... 9 However , we find that y1 = w ( z ) or , equivalently , u1 ( x1 , x2 ,. Xn ) ... depend upon 0 , the factorization theorem implies that Z = u ( Y1 ) is also ... depend upon 0. We say this because every function Z = u ( Y1 ) with a single ...
Page 344
... 9 0m . It is Ym is of m m ym ) exp , p , ( 0 . 9 0m ) y ; + nq ( 01 , 0m ) ( 2 ) R ( y1 , ... , ym ) exp at points ... depend upon any or all of the parameters 01 , 02 , ... , 0m . Moreover , in accordance with a theorem in analysis , it ...
... 9 0m . It is Ym is of m m ym ) exp , p , ( 0 . 9 0m ) y ; + nq ( 01 , 0m ) ( 2 ) R ( y1 , ... , ym ) exp at points ... depend upon any or all of the parameters 01 , 02 , ... , 0m . Moreover , in accordance with a theorem in analysis , it ...
Page 359
... depend upon 0. Thus Y = Y / n , a complete sufficient statistic for 0 , is ... 9 , n be independent is that Σa , = 0 . 1 1 7.60 . Let X and Y be random ... 9 , 0 < x < ∞ , zero elsewhere . < 2 ... ... n 7.63 . Let Y , Y2 << Y , be the ...
... depend upon 0. Thus Y = Y / n , a complete sufficient statistic for 0 , is ... 9 , n be independent is that Σa , = 0 . 1 1 7.60 . Let X and Y be random ... 9 , 0 < x < ∞ , zero elsewhere . < 2 ... ... n 7.63 . Let Y , Y2 << Y , be the ...
Other editions - View all
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