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. |
From inside the book
Results 1-3 of 89
Page 12
... definition , we consider the relative frequency approach to probability . Remark 1.3.1 . The definition of probability consists of three axioms which we will motivate by the following three intuitive properties of relative frequency ...
... definition , we consider the relative frequency approach to probability . Remark 1.3.1 . The definition of probability consists of three axioms which we will motivate by the following three intuitive properties of relative frequency ...
Page 33
... definition of a random variable and its space . Definition 1.5.1 . Consider a random experiment with a sample space C. A func- tion X , which assigns to each element c E C one and only one number X ( c ) = x , is called a random ...
... definition of a random variable and its space . Definition 1.5.1 . Consider a random experiment with a sample space C. A func- tion X , which assigns to each element c E C one and only one number X ( c ) = x , is called a random ...
Page 367
... ( Definition 4.2.2 ) of 0 if Yn converges to in probability ; i.e. , Yn is close to for large sample sizes . This is definitely a desirable property of a point estimator . Under suitable conditions , Theorem 6.1.3 shows that the maximum ...
... ( Definition 4.2.2 ) of 0 if Yn converges to in probability ; i.e. , Yn is close to for large sample sizes . This is definitely a desirable property of a point estimator . Under suitable conditions , Theorem 6.1.3 shows that the maximum ...
Contents
Some Elementary Statistical Inferences | 5 |
Multivariate Distributions | 73 |
Some Special Distributions | 133 |
Copyright | |
14 other sections not shown
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