Introduction to Mathematical StatisticsThis classic book retains its outstanding ongoing features and continues to provide readers with excellent background material necessary for a successful understanding of mathematical statistics.Chapter topics cover classical statistical inference procedures in estimation and testing, and an in-depth treatment of sufficiency and testing theory—including uniformly most powerful tests and likelihood ratios. Many illustrative examples and exercises enhance the presentation of material throughout the book.For a more complete understanding of mathematical statistics. |
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Page 397
... MVUE is bad . That is not the case at all . We merely wish to point out that if one tries hard enough , one can find ... MVUE of 02 . Hint : First determine E ( X2 ) . 7.6.2 . Let X1 , X2 , ... , Xn denote a random sample from a ...
... MVUE is bad . That is not the case at all . We merely wish to point out that if one tries hard enough , one can find ... MVUE of 02 . Hint : First determine E ( X2 ) . 7.6.2 . Let X1 , X2 , ... , Xn denote a random sample from a ...
Page 398
... MVUE of P ( X ≤ 2 ) . 7.6.8 . Let X1 , X2 , ... , Xn be a random sample with the common pdf f ( x ) = 0-1e - x / 0 , for x > 0 , zero elsewhere ; that is , f ( x ) is a г ( 1,0 ) pdf . -1 ( a ) Show that the statistic X = n1 X is a ...
... MVUE of P ( X ≤ 2 ) . 7.6.8 . Let X1 , X2 , ... , Xn be a random sample with the common pdf f ( x ) = 0-1e - x / 0 , for x > 0 , zero elsewhere ; that is , f ( x ) is a г ( 1,0 ) pdf . -1 ( a ) Show that the statistic X = n1 X is a ...
Page 403
... MVUE of p , is the statistic n ̄1Yj . Next , we shall find the MVUE of p¡pi , for j ‡ 1. Exercise 7.7.8 shows that the mle of pjp is n - 2YY . Recall from Section 3.1 that the conditional distribution of Y given Y is b ( n − Yi ) , Pj ...
... MVUE of p , is the statistic n ̄1Yj . Next , we shall find the MVUE of p¡pi , for j ‡ 1. Exercise 7.7.8 shows that the mle of pjp is n - 2YY . Recall from Section 3.1 that the conditional distribution of Y given Y is b ( n − Yi ) , Pj ...
Contents
Some Elementary Statistical Inferences | 5 |
Multivariate Distributions | 73 |
Some Special Distributions | 133 |
Copyright | |
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Other editions - View all
Introduction to Mathematical Statistics Robert V. Hogg,Joseph W. McKean,Allen Thornton Craig No preview available - 2005 |
Introduction to Mathematical Statistics Robert V. Hogg,Hogg,Joseph W. McKean,Allen T. Craig No preview available - 2013 |
Common terms and phrases
approximate asymptotic Bayes bootstrap C₁ C₂ chi-square distribution compute conditional pdf confidence interval Consider continuous random variable continuous type correlation coefficient critical region defined degrees of freedom denote a random determine discrete random variable discrete type discussed equal equation Example Exercise Find Fx(x gamma distribution given H₁ Hence independent random variables inequality integral joint pdf Let the random Let X1 Let Y₁ likelihood function linear marginal pdf matrix median MVUE normal distribution observations obtain order statistics p-value P(C₁ p₁ pdf f(x pdf of Y₁ Poisson distribution Proof random sample random variables X1 random vector respectively result S-PLUS sample mean sample space sequence Show significance level subsets sufficient statistic Suppose t-distribution test statistic Theorem unbiased estimator Wilcoxon X₁ X1 and X2 Y₁ Y₂ zero elsewhere σ²