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 234
... random and record the number . Let X denote the number . Then the distribution of X is given by 1 P ( X = x ) = for ... sample of n balls , which we will denote as X = ( X1 , ... , Xn ) ' , where X is the number on the ith ball . Now the ...
... random and record the number . Let X denote the number . Then the distribution of X is given by 1 P ( X = x ) = for ... sample of n balls , which we will denote as X = ( X1 , ... , Xn ) ' , where X is the number on the ith ball . Now the ...
Page 248
... random sample of size 4 from the uniform distribution having the pdf f ( x ) = 1 , 0 < x < 1 , zero elsewhere , is less than . = 5.2.12 . Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 from a distribution having ...
... random sample of size 4 from the uniform distribution having the pdf f ( x ) = 1 , 0 < x < 1 , zero elsewhere , is less than . = 5.2.12 . Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 from a distribution having ...
Page 260
... random sample from the distribution of Y. As above , assume that the samples are independent of one another and let n = n1 + n2 be the total sample size . Our estimator of p1 P2 is the difference in sample proportions which , of course ...
... random sample from the distribution of Y. As above , assume that the samples are independent of one another and let n = n1 + n2 be the total sample size . Our estimator of p1 P2 is the difference in sample proportions which , of course ...
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