Introduction to Mathematical Statistics and Its Applications, An

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9780134871745: Introduction to Mathematical Statistics and Its Applications, An

This volume allows those with an established mathematics background to pursue a more rigorous treatment of probability and statistics.

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From the Publisher:

Highly structured, this volume allows those with an established mathematics background to pursue a more rigorous, advanced treatment of probability and statistics.

From the Inside Flap:

Preface

Changes in this third edition have been primarily motivated by our own teaching experiences as well as by the comments of others who use the text. Technology, though, has also dictated certain revisions. The widespread use of statistical software packages has brought certain topics and concepts to the fore, while diminishing the relevance of others. All in all, we feel that this new edition has a sharper focus and that students will find it more accessible and easier to use.

Many of the major changes come in the middle third of the book, much of which has been rewritten. These are the chapters that make the critical transition from probability to statistics. We have taken a variety of steps to make that material come more alive, ranging from the addition of more helpful examples to the frequent use of computer simulations.

Chapter 4, for example, now addresses more fully the important question of why certain measurements are modeled by particular probability functions. Relationships that exist between pdfs are given more attention, and the connection between theoretical models and sample data is explored in greater depth. Chapter 5 has been restructured. In the new edition, methods of estimation come first and the underlying theory is taken up last. That arrangement makes it easier for instructors to adjust the amount of time spent on estimation to whatever suits their individual needs. In Chapter 6, the principles of decision-making are now introduced in the context of testing Ho: µ = µo rather than Ho: p = po. The result is a more streamlined presentation that avoids the complications inherent in a test statistic whose pdf is discrete.

Positioned between Chapter 7, which deals with the normal distribution, and Chapters 9 through 14, where the various techniques for analyzing data are introduced, is a new chapter on experimental design. Chapter 8 profiles seven of the most frequently encountered "data models." The basic characteristics of each design are discussed as well as the types of questions each seeks to answer. By providing a framework and a theme, Chapter 8 brings cohesion and a sense of order to the chapters that follow.

Chapter 11 (Regression) has also been changed substantially. It now begins with curve-fitting, then introduces the linear model, and eventually concludes with the bivariate normal. Regression "diagnostics" have been added to the new edition, and the various inference procedures associated with the linear model have been explained and delineated more carefully.

Our overriding motivation in deciding which topics to present – and in what order – stem from our objective to write a book that emphasizes the interrelation between probability theory, mathematical statistics, and data analysis. We believe that integrating all three is vitally important, particularly for those students who take only one statistics course during their college careers. Our experience in the classroom has certainly strengthened our faith in this approach: Students can more clearly see the importance of each of the three when viewed in the context of the other two.

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Richard J. Larsen
Published by Prentice Hall College Div (1985)
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