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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Results 1-3 of 51
Page 149
... integral e -1 -y dy exists for a > 0 and that the value of the integral is a positive number . The integral is called the gamma function of a , and we write = If a 1 , clearly г ( a ) = 1 - le - dy a - 1e - y dy . г ( 1 ) = • ∞ e- " dy ...
... integral e -1 -y dy exists for a > 0 and that the value of the integral is a positive number . The integral is called the gamma function of a , and we write = If a 1 , clearly г ( a ) = 1 - le - dy a - 1e - y dy . г ( 1 ) = • ∞ e- " dy ...
Page 153
... integral like P ( X ≤ x ) = [ * 1 г ( r / 2 ) 2r / 2 - -w / 2 dw . Tables of this integral for selected values of r and x have been prepared and are partially reproduced in Table II in Appendix C. If , on the other hand , the package R ...
... integral like P ( X ≤ x ) = [ * 1 г ( r / 2 ) 2r / 2 - -w / 2 dw . Tables of this integral for selected values of r and x have been prepared and are partially reproduced in Table II in Appendix C. If , on the other hand , the package R ...
Page 161
... integral we made the one - to - one change of variable w = z - t . By the identity ( 3.4.2 ) , the integral in expression ( 3.4.3 ) has value 1. Thus the mgf of Z is : Mz ( t ) = exp 信 for ∞ < t < ∞ . The first two derivatives of Mz ...
... integral we made the one - to - one change of variable w = z - t . By the identity ( 3.4.2 ) , the integral in expression ( 3.4.3 ) has value 1. Thus the mgf of Z is : Mz ( t ) = exp 信 for ∞ < t < ∞ . The first two derivatives of Mz ...
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