Introduction to Mathematical Statistics |
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Page ix
... Maximum Likelihood Estimation of Parameters 243 9.3 Decision Functions 248 9.4 Bayesian Procedures . 250 Chapter 10 STATISTICAL HYPOTHESES 10.1 Some Examples and Definitions 254 254 10.2 Certain Best Tests 261 10.3 Uniformly Most ...
... Maximum Likelihood Estimation of Parameters 243 9.3 Decision Functions 248 9.4 Bayesian Procedures . 250 Chapter 10 STATISTICAL HYPOTHESES 10.1 Some Examples and Definitions 254 254 10.2 Certain Best Tests 261 10.3 Uniformly Most ...
Page 246
... maximum likelihood statistics exist , then these maxi- mum likelihood statistics are functions of the joint sufficient statistics . An illustrative example follows . 2 Example 4. Let X1 , X2 , ... , X , denote a random sample from a ...
... maximum likelihood statistics exist , then these maxi- mum likelihood statistics are functions of the joint sufficient statistics . An illustrative example follows . 2 Example 4. Let X1 , X2 , ... , X , denote a random sample from a ...
Page 247
... maximum likelihood statistic for 0. If a sufficient statistic Y also exists , express & as a function of Y. -- 9.8 . Let X1 , X2 , ... , X2 be a random sample from the distribution having ... Maximum Likelihood Estimation of Parameters 247.
... maximum likelihood statistic for 0. If a sufficient statistic Y also exists , express & as a function of Y. -- 9.8 . Let X1 , X2 , ... , X2 be a random sample from the distribution having ... Maximum Likelihood Estimation of Parameters 247.
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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