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 69
... inequality that is often called Chebyshev's inequality . This inequality will now be established . Theorem 1.10.3 ( Chebyshev's Inequality ) . Let the ... inequality , this probability has the upper bound 1.10 . Important Inequalities 69.
... inequality that is often called Chebyshev's inequality . This inequality will now be established . Theorem 1.10.3 ( Chebyshev's Inequality ) . Let the ... inequality , this probability has the upper bound 1.10 . Important Inequalities 69.
Page 70
... inequality . □ = - --- In each of the instances in the preceding example , the probability P ( | X − μ | ≥ ko ) and its upper bound 1 / k2 differ considerably . This suggests that this inequality might be made sharper . However , if ...
... inequality . □ = - --- In each of the instances in the preceding example , the probability P ( | X − μ | ≥ ko ) and its upper bound 1 / k2 differ considerably . This suggests that this inequality might be made sharper . However , if ...
Page 71
... inequality will be strict if ( " ( x ) > 0 , for all x € ( a , b ) , provided X is not a constant . □ Example 1.10.3 . Let X be a nondegenerate random variable with mean ... inequality is called the harmonic 1.10 . Important Inequalities 71.
... inequality will be strict if ( " ( x ) > 0 , for all x € ( a , b ) , provided X is not a constant . □ Example 1.10.3 . Let X be a nondegenerate random variable with mean ... inequality is called the harmonic 1.10 . Important Inequalities 71.
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