Modern Concepts and Theorems of Mathematical Statistics

1. Front Matter

   Pages i-xvi

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2. Fundamentals of Mathematical Statistics

   1. Front Matter

      Pages 1-1

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   2. Basic Definitions, Concepts, Results, and Theorems

      • Edward B. Manoukian

      Pages 3-74

   3. Fundamental Limit Theorems

      • Edward B. Manoukian

      Pages 75-98

3. Statistical Distributions

   1. Front Matter

      Pages 99-99

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   2. Distributions

      • Edward B. Manoukian

      Pages 101-131

   3. Some Relations Between Distributions

      • Edward B. Manoukian

      Pages 132-144

4. Back Matter

   Pages 145-149

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With the rapid progress and development of mathematical statistical methods, it is becoming more and more important for the student, the in­ structor, and the researcher in this field to have at their disposal a quick, comprehensive, and compact reference source on a very wide range of the field of modern mathematical statistics. This book is an attempt to fulfill this need and is encyclopedic in nature. It is a useful reference for almost every learner involved with mathematical statistics at any level, and may supple­ ment any textbook on the subject. As the primary audience of this book, we have in mind the beginning busy graduate student who finds it difficult to master basic modern concepts by an examination of a limited number of existing textbooks. To make the book more accessible to a wide range of readers I have kept the mathematical language at a level suitable for those who have had only an introductory undergraduate course on probability and statistics, and basic courses in calculus and linear algebra. No sacrifice, how­ ever, is made to dispense with rigor. In stating theorems I have not always done so under the weakest possible conditions. This allows the reader to readily verify if such conditions are indeed satisfied in most applications given in modern graduate courses without being lost in extra unnecessary mathematical intricacies. The book is not a mere dictionary of mathematical statistical terms.

• Estimator
• Likelihood
• Median
• Random variable
• Statistics
• Theorems
• Variance
• best fit
• correlation
• mathematical statistics

• Department of National Defence, Royal Military College of Canada, Kingston, Canada

  Edward B. Manoukian

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