Introduction to Mathematical Statistics |
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Page 222
... probability density functions be complete . If there is a continuous function of Y1 which is an unbiased statistic for 0 , then this function of Y1 is the unique best statistic for 0. Here " unique " is used in the sense described in ...
... probability density functions be complete . If there is a continuous function of Y1 which is an unbiased statistic for 0 , then this function of Y1 is the unique best statistic for 0. Here " unique " is used in the sense described in ...
Page 223
... function of this statistic that is the best statistic for 0 . 8.7 The Exponential Class of Probability Density Functions Consider a family { ƒ ( x ; 0 ) ; 0 = N } of probability density functions , where is the interval set = { 0 ; y ...
... function of this statistic that is the best statistic for 0 . 8.7 The Exponential Class of Probability Density Functions Consider a family { ƒ ( x ; 0 ) ; 0 = N } of probability density functions , where is the interval set = { 0 ; y ...
Page 228
... probability density functions is generalized as follows : Let 1 , { f ( V1 , V2 , ... , Vk ; 01 , 02 , ... , 0m ) ; ( 01 , 02 , ... , ... , . θη ) ΕΩ } ... ) m denote a family of probability density functions of k random variables V1 ...
... probability density functions is generalized as follows : Let 1 , { f ( V1 , V2 , ... , Vk ; 01 , 02 , ... , 0m ) ; ( 01 , 02 , ... , ... , . θη ) ΕΩ } ... ) m denote a family of probability density functions of k random variables V1 ...
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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 oČ w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ