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 201
... order statistics of a random sample of size 4 from the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Find Pr ( 3 Y1 ) . 4.57 . Let X1 , X2 , X , be a random sample from a distribution of ... Order Statistics 201.
... order statistics of a random sample of size 4 from the distribution having p.d.f. f ( x ) = e ̄ * , 0 < x < ∞ , zero elsewhere . Find Pr ( 3 Y1 ) . 4.57 . Let X1 , X2 , X , be a random sample from a distribution of ... Order Statistics 201.
Page 499
... order 0.25 ) of the distribution . Since ( n + 1 ) p = 28 ( ) = 7 , the seventh order statistic , y , 83 , could serve as a point estimate of $ 0.25 . To get a confidence interval for 0.25 , consider two order statistics , one less than ...
... order 0.25 ) of the distribution . Since ( n + 1 ) p = 28 ( ) = 7 , the seventh order statistic , y , 83 , could serve as a point estimate of $ 0.25 . To get a confidence interval for 0.25 , consider two order statistics , one less than ...
Page 500
... order statistics of a random sample of size 9 from a distribution of the continuous type . 11.4 . Find the smallest value of n for which Pr ( Y1 < 50.5 < Yn ) ≥ 0.99 , where Y1 < < Y , are the order statistics of a random sample of ...
... order statistics of a random sample of size 9 from a distribution of the continuous type . 11.4 . Find the smallest value of n for which Pr ( Y1 < 50.5 < Yn ) ≥ 0.99 , where Y1 < < Y , are the order statistics of a random sample of ...
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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