Introduction to Mathematical Statistics |
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Page 100
... statistics of this random sample . We shall show that Y is a sufficient statistic for 0. From Section 4.6 , page 85 , the joint p.d.f. of Y1 , Y2 , Yз , Y4 is g ( Y1 , Y2 , Yз , Y4 ; 0 ) 4 ! = " 04 0 < Yi < Y2 < Y3 < Y4 < 0 ...
... statistics of this random sample . We shall show that Y is a sufficient statistic for 0. From Section 4.6 , page 85 , the joint p.d.f. of Y1 , Y2 , Yз , Y4 is g ( Y1 , Y2 , Yз , Y4 ; 0 ) 4 ! = " 04 0 < Yi < Y2 < Y3 < Y4 < 0 ...
Page 101
... statistic for 0. For convenience , let X3 and Y3 X3 , so by the corresponding transformation the space = = that Yı Y2 ... yi , does not depend upon so that Y1 is a sufficient statistic for 0 . 5.12 . If X1 , X2 is a random sample of size ...
... statistic for 0. For convenience , let X3 and Y3 X3 , so by the corresponding transformation the space = = that Yı Y2 ... yi , does not depend upon so that Y1 is a sufficient statistic for 0 . 5.12 . If X1 , X2 is a random sample of size ...
Page 103
... statistic Y1 is 1 by fermia P. 154 ∞ 91 ( Y1 ; 0 ) = 31 Ya = ne ... " = 0 ... sufficient statistic for 0 . = 2 1 Before taking the next step in our search ... ( Yi ) is also a suffi cient statistic for 0 . Exercises 5.13 . Show that the ...
... statistic Y1 is 1 by fermia P. 154 ∞ 91 ( Y1 ; 0 ) = 31 Ya = ne ... " = 0 ... sufficient statistic for 0 . = 2 1 Before taking the next step in our search ... ( Yi ) is also a suffi cient statistic for 0 . Exercises 5.13 . Show that the ...
Contents
CHAPTER | 1 |
TRANSFORMATION OF VARIABLES cont | 17 |
CHAPTER | 27 |
Copyright | |
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A₁ A₂ best critical region binomial distribution c₁ cent confidence interval chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type critical region degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean EXAMPLE Exercises function of Y₁ hypothesis H₁ independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(x null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Y₁ p₁ Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions r₁ random experiment random sample random variables X1 Show significance level statistical hypothesis stochastically independent random theorem type of random unbiased statistic values variance o² X₁ X1 and X2 X₂ Xn denote Y₂ zero elsewhere μ₁ σ²