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 332
... probability density functions be complete . If there is a function of Y , that is an unbiased estimator of 0 , then this function of Y is the unique unbiased minimum variance estimator of 0. Here “ unique ” is used in the sense ...
... probability density functions be complete . If there is a function of Y , that is an unbiased estimator of 0 , then this function of Y is the unique unbiased minimum variance estimator of 0. Here “ unique ” is used in the sense ...
Page 333
... density functions { h ( z ; 0 ) : 0 ≤ N } , where h ( z ; 0 ) = 1/0 , 0 ≤ z < 0 , zero elsewhere . ( a ) Show that the family is complete provided ... Probability Density Functions 333 The Exponential Class of Probability Density Functions.
... density functions { h ( z ; 0 ) : 0 ≤ N } , where h ( z ; 0 ) = 1/0 , 0 ≤ z < 0 , zero elsewhere . ( a ) Show that the family is complete provided ... Probability Density Functions 333 The Exponential Class of Probability Density Functions.
Page 335
Robert V. Hogg, Allen Thornton Craig. at points of positive probability density . The points of positive probability density and the function R ( y , ) do not depend upon 0 . At this time we use a theorem ... Probability Density Functions ...
Robert V. Hogg, Allen Thornton Craig. at points of positive probability density . The points of positive probability density and the function R ( y , ) do not depend upon 0 . At this time we use a theorem ... Probability Density Functions ...
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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 g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ 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 sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²