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 < ∞o , zero elsewhere . Find Pr ( 3≤ Y1 ) . 3 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 < ∞o , zero elsewhere . Find Pr ( 3≤ Y1 ) . 3 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 ( 4 ) = 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 ...
... order 0.25 ) of the distribution . Since ( n + 1 ) p = 28 ( 4 ) = 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 ...
Page 505
... order statistics partition the probability for the distribution into n + 1 parts , and the expected value of each of these parts is 1 / ( n + 1 ) . More generally , the expected value of F ( Y ) - F ( Y ) , i < j , is ( j — i ) / ( n + ...
... order statistics partition the probability for the distribution into n + 1 parts , and the expected value of each of these parts is 1 / ( n + 1 ) . More generally , the expected value of F ( Y ) - F ( Y ) , i < j , is ( j — i ) / ( n + ...
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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. 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