Introduction to Mathematical Statistics |
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Page 288
... ratio of L ( ŵ ) to L ( ÔN ) is called the likeli- hood ratio and is denoted by X ( X1 , X2 ,. xn ) = λ = L ( w ) L ( Q ) Let λo be a positive proper fraction . The likelihood ratio test principle states that the hypothesis Ho : ( 01 ...
... ratio of L ( ŵ ) to L ( ÔN ) is called the likeli- hood ratio and is denoted by X ( X1 , X2 ,. xn ) = λ = L ( w ) L ( Q ) Let λo be a positive proper fraction . The likelihood ratio test principle states that the hypothesis Ho : ( 01 ...
Page 293
... ratio principle leads to the same test , when testing a simple hypothesis H。 against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there only two points in Q. 11.4 . Verify Equations ...
... ratio principle leads to the same test , when testing a simple hypothesis H。 against an alternative simple hypothesis H1 , as that given by the Neyman - Pearson theorem . Note that there only two points in Q. 11.4 . Verify Equations ...
Page 298
... ratio for testing Ho : 01 04 against all alternatives = მე , ძვ = is given by ( x + - x ) 2 / n n / 2 m m / 2 ( y . - ÿ ) 2 / m where u = ( x + ― m u ) 2 + { ( y , − u ) 2 ] / ( m + n ) } ( n + m ) / 2 ( nã + mỹ ) / ( n + m ) . ( b ) ...
... ratio for testing Ho : 01 04 against all alternatives = მე , ძვ = is given by ( x + - x ) 2 / n n / 2 m m / 2 ( y . - ÿ ) 2 / m where u = ( x + ― m u ) 2 + { ( y , − u ) 2 ] / ( m + n ) } ( n + m ) / 2 ( nã + mỹ ) / ( n + m ) . ( b ) ...
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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