Introduction to Mathematical Statistics |
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Page 60
Robert V. Hogg, Allen Thornton Craig. We shall next extend the definition of a conditional p.d.f. If f ( x1 ) 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the relation > f ( x2 , .. xnx1 ) = f ( x1 , x2 , . . . , Xn ) f1 ( x1 ) and ...
Robert V. Hogg, Allen Thornton Craig. We shall next extend the definition of a conditional p.d.f. If f ( x1 ) 0 , the symbol f ( x2 , ... , xnx1 ) is defined by the relation > f ( x2 , .. xnx1 ) = f ( x1 , x2 , . . . , Xn ) f1 ( x1 ) and ...
Page 258
... Definition 4. The power function of a test of a statistical hypothesis H。 against an alternative hypothesis H1 is that function , defined for all distributions under consideration , which yields the probability that the sample point ...
... Definition 4. The power function of a test of a statistical hypothesis H。 against an alternative hypothesis H1 is that function , defined for all distributions under consideration , which yields the probability that the sample point ...
Page 295
... defined by λ is a function of the statistic n Ž ( X , − X ) 2 / ( n − 1 ) - = F 1 = m ( Yi - Y ) 2 / ( m − 1 ) ... defined by the likelihood ratio L ( w ) / L ( ŵ1 ) . However , this is exactly the problem presented in Example 2 of ...
... defined by λ is a function of the statistic n Ž ( X , − X ) 2 / ( n − 1 ) - = F 1 = m ( Yi - Y ) 2 / ( m − 1 ) ... defined by the likelihood ratio L ( w ) / L ( ŵ1 ) . However , this is exactly the problem presented in Example 2 of ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²