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 308
... unbiased estimator of 0 . For illustration , let X1 , X2 , ... , X , denote a random sample from a distribution that is N ( 0 , 1 ) , ∞ < 0 < ∞o . Since the statistic X = ( X1 + X 2 + · · · + X9 ) / 9 is N ( 0 , 4 ) , X is an unbiased ...
... unbiased estimator of 0 . For illustration , let X1 , X2 , ... , X , denote a random sample from a distribution that is N ( 0 , 1 ) , ∞ < 0 < ∞o . Since the statistic X = ( X1 + X 2 + · · · + X9 ) / 9 is N ( 0 , 4 ) , X is an unbiased ...
Page 326
... unbiased point estimates of parameters . In showing this , we can refer back to a result of Section 2.2 : If X , and X1⁄2 are random variables and certain ... unbiased estimator Y2 in their search for 326 Sufficient Statistics [ Ch . 7.
... unbiased point estimates of parameters . In showing this , we can refer back to a result of Section 2.2 : If X , and X1⁄2 are random variables and certain ... unbiased estimator Y2 in their search for 326 Sufficient Statistics [ Ch . 7.
Page 327
Robert V. Hogg, Allen Thornton Craig. 2 first some unbiased estimator Y2 in their search for ø ( Y1 ) , an unbiased estimator of @ based upon the sufficient statistic Y1 . This is not the case at all , and Theorem 3 simply convinces us ...
Robert V. Hogg, Allen Thornton Craig. 2 first some unbiased estimator Y2 in their search for ø ( Y1 ) , an unbiased estimator of @ based upon the sufficient statistic Y1 . This is not the case at all , and Theorem 3 simply convinces us ...
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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