Introduction to Mathematical Statistics |
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Page 222
... complete , the continuous function ( ၅ ) ( y ) = 0 at each point y , at which at least one member of the family is positive . That is , at all points of nonzero probability density , we have , for every continuous unbiased statistic ...
... complete , the continuous function ( ၅ ) ( y ) = 0 at each point y , at which at least one member of the family is positive . That is , at all points of nonzero probability density , we have , for every continuous unbiased statistic ...
Page 225
... complete sufficient statistic for the mean of a normal distribution for every given value of the variance o2 . Since E ( Y ) = no , then ( Y1 ) = Y1 / n X is the only continuous function of Y1 that is an unbiased statistic for 0 ; and ...
... complete sufficient statistic for the mean of a normal distribution for every given value of the variance o2 . Since E ( Y ) = no , then ( Y1 ) = Y1 / n X is the only continuous function of Y1 that is an unbiased statistic for 0 ; and ...
Page 233
... complete . That is , the theorem may not be stated as an “ if , and only if , " condition for the stochastic independence of the statistic Z and the sufficient statistic Y1 . However , if we restrict ƒ ( x ; 0 ) to represent a regular ...
... complete . That is , the theorem may not be stated as an “ if , and only if , " condition for the stochastic independence of the statistic Z and the sufficient statistic Y1 . However , if we restrict ƒ ( x ; 0 ) to represent a regular ...
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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