Introduction to Mathematical Statistics |
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Page 168
Robert V. Hogg, Allen Thornton Craig. Order Statistics 6.1 Distributions of Order Statistics In this section the notion of an order statistic will be defined and we shall investigate some of the simpler properties of such a statistic ...
Robert V. Hogg, Allen Thornton Craig. Order Statistics 6.1 Distributions of Order Statistics In this section the notion of an order statistic will be defined and we shall investigate some of the simpler properties of such a statistic ...
Page 176
... order statistics of a random sample of size 3 from the distribution having p.d.f. f ( x ) = e− ( x − 0 ) , 0 < x < ∞ , zero elsewhere , where ∞ << ∞ . Determine the function c ( 0 ) of @ so that Pr [ 0 < Y1 < c ( 0 ) ] = 0.95 ...
... order statistics of a random sample of size 3 from the distribution having p.d.f. f ( x ) = e− ( x − 0 ) , 0 < x < ∞ , zero elsewhere , where ∞ << ∞ . Determine the function c ( 0 ) of @ so that Pr [ 0 < Y1 < c ( 0 ) ] = 0.95 ...
Page 182
... order statistics of a random sample of size 5 from a distribution of the continuous type . Compute ( a ) Pr ( Y1 < 0.5 < Y5 ) ; 1 ( b ) Pr ( Y1 < $ 0.25 < Y3 ) ; 1 ( c ) Pr ( Y4 < $ 0.80 < Y5 ) . 1 9 6.17 . Compute Pr ( Y3 < 0.5 < Y1 ) ...
... order statistics of a random sample of size 5 from a distribution of the continuous type . Compute ( a ) Pr ( Y1 < 0.5 < Y5 ) ; 1 ( b ) Pr ( Y1 < $ 0.25 < Y3 ) ; 1 ( c ) Pr ( Y4 < $ 0.80 < Y5 ) . 1 9 6.17 . Compute Pr ( Y3 < 0.5 < Y1 ) ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ