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 322
... sufficient statistic for 0 . 1 7.14 . Show that the sum of the observations of a random sample of size n from a gamma distribution that has p.d.f. f ( x ; 0 ) = ( 1/0 ) ... Sufficient Statistics [ Ch . 7 Properties of a Sufficient Statistic.
... sufficient statistic for 0 . 1 7.14 . Show that the sum of the observations of a random sample of size n from a gamma distribution that has p.d.f. f ( x ; 0 ) = ( 1/0 ) ... Sufficient Statistics [ Ch . 7 Properties of a Sufficient Statistic.
Page 348
... statistic for one parameter or two joint sufficient statistics for two parameters . Possibly the most complicated case considered so far is given in Exercise 7.48 , in which we find five joint sufficient ... Sufficient Statistics [ Ch . 7.
... statistic for one parameter or two joint sufficient statistics for two parameters . Possibly the most complicated case considered so far is given in Exercise 7.48 , in which we find five joint sufficient ... Sufficient Statistics [ Ch . 7.
Page 352
... statistics provide good illustrations , with the appropriate model for the p.d.f. , of ancillary statistics . Since an ancillary statistic and a complete ( minimal ) sufficient statistic are such opposites , we might believe that there ...
... statistics provide good illustrations , with the appropriate model for the p.d.f. , of ancillary statistics . Since an ancillary statistic and a complete ( minimal ) sufficient statistic are such opposites , we might believe that there ...
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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. 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