Product Description
Approximation Theorems of Mathematical Statistics

This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory.

The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of:

• The tools and foundations that are basic to asymptotic theory in statistics
• The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence
• Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding’s U-statistics and R. von Mises’s "differentiable statistical functions"
• Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics")
• Use of influence curves
• Approaches toward asymptotic relative efficiency of statistical test procedures

Customer Reviews (1)

Great Reference
As a graduate student in statistics, I have had plenty of opportunities to browse through the pages of this book in search of that theorem, technique, or tool that would be applicable to my own work.In many occasions I was succesful in such search.This title compiles and synthesizes a wealth of definitions, theorems, and techniques classically used in asymptotic theory of estimators.It is as much as possible a self-contained work with enough introductory material to be used independently of other references.A bit outdated now, and with minimal material on dependent random variables, this title is still a classic compendium on statistical approximation theory. ... Read more

Product Description
Now updated in a valuable new edition—this user-friendly book focuses on understanding the "why" of mathematical statistics

Probability and Statistical Inference, Second Edition introduces key probability and statis-tical concepts through non-trivial, real-world examples and promotes the developmentof intuition rather than simple application. With its coverage of the recent advancements in computer-intensive methods, this update successfully provides the comp-rehensive tools needed to develop a broad understanding of the theory of statisticsand its probabilistic foundations. This outstanding new edition continues to encouragereaders to recognize and fully understand the why, not just the how, behind the concepts,theorems, and methods of statistics. Clear explanations are presented and appliedto various examples that help to impart a deeper understanding of theorems and methods—from fundamental statistical concepts to computational details.

Additional features of this Second Edition include:

• A new chapter on random samples

• Coverage of computer-intensive techniques in statistical inference featuring Monte Carlo and resampling methods, such as bootstrap and permutation tests, bootstrap confidence intervals with supporting R codes, and additional examples available via the book's FTP site

• Treatment of survival and hazard function, methods of obtaining estimators, and Bayes estimating

• Real-world examples that illuminate presented concepts

• Exercises at the end of each section

Providing a straightforward, contemporary approach to modern-day statistical applications, Probability and Statistical Inference, Second Edition is an ideal text for advanced undergraduate- and graduate-level courses in probability and statistical inference. It also serves as a valuable reference for practitioners in any discipline who wish to gain further insight into the latest statistical tools. ... Read more

Customer Reviews (2)

Good Intro to probability theory and statistics
I found this book quite thorough and very well written. I liked it a lot because, although not advanced, it does not lack mathematical rigour. I thouroughly recommended for anybody who needs a sound basis for probability and statistics.

Good Intro to probability theory and statistics
I found this book quite thorough and very well written. I liked it a lot because, although not advanced, it does not lack mathematical rigour. I thouroughly recommended for anybody who needs a sound basis for probability and statistics. ... Read more

Product Description
In this classic of statistical mathematical theory, Harald Cramér joins the two major lines of development in the field: while British and American statisticians were developing the science of statistical inference, French and Russian probabilitists transformed the classical calculus of probability into a rigorous and pure mathematical theory. The result of Cramér's work is a masterly exposition of the mathematical methods of modern statistics that set the standard that others have since sought to follow.

For anyone with a working knowledge of undergraduate mathematics the book is self contained. The first part is an introduction to the fundamental concept of a distribution and of integration with respect to a distribution. The second part contains the general theory of random variables and probability distributions while the third is devoted to the theory of sampling, statistical estimation, and tests of significance. ... Read more

Customer Reviews (4)

the first great book on mathematical statistics
Princeton University Press originally published this book in the mid 1940s. At the time, Harold Cramer was a leading statistician in Sweden. The field of mathematical statistics was just being formalized and there were no existing books with good mathematical treatment of inference methods. Kolmogorov was developing a rigorous measure theoretic basis for probability while Fisher and Neyman were developing different schools of thought on statistical inference.
Cramer put together the standard reference on mathematical statistics which is still valuable today. This is the type of book to be enjoyed by mathematical statisticians looking at it from a historical perspective. Recent advances require those who need a modern course to study other texts.
Mathematical Statistics made great strides in the 1940s through the 1970s in Europe and America and continues to grow even today.A lot of the the mathematical research in the development of statistical theory can be atrributed to the publication of Cramer's book

not the best book ...
This book is a very old edition. The print quality is not that good. The book is target to real mathematicians, interested in the abstract foundations of probability. I think this was an excellent book in the past, but currently I found a much better book : 'Real analysis and probability' by R.M. Dudley. Dudley 's book is more modern, for instance mentioning banach spaces as the framework for probability. Dudley 's book also provides more rigor and is even more self contained. Cramers book is definetely a 'nice to have' for historical reasons, but if you want an excellent complete explanation of the abstract probability theory, then you definitely must read Dudley ....

not the best book ...
This book is a very old edition. The print quality is not that good. The book is target to real mathematicians, interested in the abstract foundations of probability. I think this was an excellent book in the past, but currently I found a much better book : 'Real analysis and probability' by R.M. Dudley. Dudley 's book is more modern, for instance mentioning banach spaces as the framework for probability. Dudley 's book also provides more rigor and is even more self contained. Cramers book is definetely a 'nice to have' for historical reasons, but if you want an excellent complete explanation of the abstract probability theory, then you definitely must read Dudley ....

A Statistical Toure de Force
This was the first textbook on modern mathematical statistics, and is still one of the best. This work was one of the key elements which transformed probability theory and statistics into rigorous and powerfulbranches of mathematics.

It begins with an introduction to the theory ofintegration and measures, assuming no more than a working knowledge ofcalculus, and is one of the best introductory expositions of measure theoryavailable.

The second part of the book is on statistical inference, andfollows the three giants of modern statistics, Fisher, Neyman and Pearson. Cramér explains the difficult subjects of confidence regions andNeyman-Pearson hypothesis testing clearly and convincingly. The closingportion of the book discuss analysis of variance and linear regressionmethods; and is supplemented with real-world examples throughout, leaningheavily on the data provided by the Swedish census.

This book is aclassic, not least for its combination of lucidity and rigor. Inrecognition of its merits, it has been re-issued in an affordable paperbackedition. It belongs on the shelf of anyone interested in statisticalmethods. ... Read more

Product Description
The Student Solutions Manual provides worked-out solutions to the selected problems in the text. ... Read more

Customer Reviews (1)

Solutions Manual
I do find this extremely helpful in checking answers and finding out where I went wrong in a problem.However, this solutions manual would be even more beneficial if it included more explanations for each step.I would definitely recommend this for the statistics book. ... Read more

Product Description
This textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed, being developed as needed. The book is committed to both a high level of mathematical seriousness and to an intimate connection with application. In its teaching style, the book is * mathematically complete * concrete * constructive * active. The text is aimed at the upper undergraduate or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite series. ... Read more

Customer Reviews (2)

Kindle version loaded with misprints
The Kindle version has so many misprints it is unreadable.They did an extremely poor job of digitization.Many of the mathematical formulae have pieces missing and in a mathematical textbook the missing pieces are fatal to comprehension.Sometimes the mathematical formulae are printed in such small type that even with a magnifying glass it is difficult to make out what they are expressing.While the Kindle allows one to enlarge text some of these formulae do not enlarge.

It looks like no one competent proof read the work after it was converted to Kindle format since I discovered these errors straight off and any one who understood mathematics would have immediately noticed the errors.

I'm surprised that such a shoddy job was let ride.Springer has an excellent reputation yet they apparently are investing no resources into the editing and proof-reading of electronic texts.

If you buy this text in Kindle form you will be unable to learn the subject matter from it and you will want your money back.

Very Good book for self-study and further motivation
This is one of the rare books in mathematical statistics which directly appeals to intuition and manages to provide some hunch (and create deep curiosity) for advanced topics. Moreover it remains always connected to emprical examples and encourages reader to engage with the data. Therefore it is very suitable for self-study.
Briefly, this book is definitely advisable to anyone who wants to know about the theory of statistics. Only small defect is that; there are some typos here and there which may sometimes be annoying. ... Read more

Product Description
This modern treatment of mathematical statistics is concise, yet detailed enough to give readers a solid foundation in all aspects of the field. Treatment of each topic is thorough enough to make the coverage self-contained for a course in probability, and exceptional care has been taken to balance theory with applications. In addition to classical probability theory, such modern topics as order statistics and limiting distributions are discussed, along with applied examples from a wide variety of fields. Discussions include the core mathematical statistics topics of estimation, testing, and confidence intervals; ranking and selection procedures; decision theory; nonparametric statistics; regression and ANOVA; and robust statistical procedures. Computer-assisted data analysis is discussed at several points, reflecting the importance of statistical computation to the field. FORTRAN programs and BMDP routines are included, as well as the highly popular SAS routines. Also looks at the potential contribution of expert systems to statistics. ... Read more

Customer Reviews (1)

good treatment of modern methods
Dudewicz and Mishra provide a good treatment of mathematical statistics as it was in 1988. It is unique in its coverage of computational methods and software and the emerging area of expert systems. I was pleased to see coverage of influence functions including some of my work. This book also provides a good mix of theory and application. ... Read more

Product Description
Stat Labs: Mathematical Statistics Through Applications blends mathematical statistics with modern statistical practice. It turns the traditional teaching of mathematical statistics on its head by making a case study the centerpiece of each chapter. Chapters begin with the introduction of a real problem followed by a description of the data collected to address the problem, rich background material to put the problem in context, and suggestions for investigating the problem. This novel approach to bringing data analysis into the theoretical course is ideal for motivating and illustrating standard statistical techniques, for helping students understand mathematical statistics, and for showing how statistics can be useful in a wide variety of contexts. Stat Labs is designed for use in a calculus-based introductory statistics course. It would be equally effective as a stand-alone text or as a supplement to a traditional mathematical statistics text. Deborah Nolan received her Ph.D in Statistics from Yale University, and she is now Professor of Statistics at the University of California, Berkeley. Her research interests include high-dimensional modeling, the teaching of statistics, and the use of technology in education. She has also been involved in encouraging women into research careers in the mathematical sciences, and in 1997 edited the volume, Women in Mathematics: Scaling the Heights for the Mathematical Association of America. Terry Speed's professional activities center around teaching and research involving th application of statistics to genetics and molecular biology. He spends 50% of his time in the Department of Statistics of the University of California at Berkeley, and the other 50% with the Genetics and Bioinformatics Group of the Walter & Eliza Hall Institute of Medical Research in Melbourne, Australia. ... Read more

Customer Reviews (2)

interesting approach to teaching statistics


I took my introductory mathematical statistics course from Brad Efron and Charles Stein at Stanford. It gave me a strong foundation and understanding of decision theory, hypothesis testing and the power of exponential families of distributions. Although I understood the Neyman - Pearson theory of hypothesis testing and confidence intervals, I was not completely comfortable applying what I had learn when confronted with real problems. Students even at the best universities in the US still need consulting experience before they are comfortable with the tools they learn.
That is why this book so intrigued me. It approaches the theory and methods from applications first. Each chapter poses an interesting real problem and then progresses to a solution, introducing only the necessary tools. Many important statistical tools and topics are covered this way. It is particularly good for students interested in biostatistics as many of the applications fall in that area. In fact the subject of maternal smoking and infant health is treated in Chapter 1 and revisited in Chapter 10 with additional data to consider.

It is designed for an advanced undergraduate course for statistics majors and has been successfully implemented by the authors at Berkeley. I think this can really work and make mathematical statistics interesting. However, the student should not think that he or she can come out of this class and jump right into consulting. The biggest problem in consulting is working with the client to pose a well formulated problems that address their questions. In this text the authors have already done that long and difficult task for us and we are left in a position to learn the subject matter and the statistical tools needed for the solution.

An Excellent Book
This book is now being used at the university I attend for a Data Analysis Course.The examples provided were used as projects for out class.I learned a lot about real world problems that can be solved and modeled using statistics.

I recommend the software MiniTAB to accompany this book.

I especially liked the chapter on HIV and mortality (very interesting results)! ... Read more

Product Description
This textbook provides a comprehensive introduction to mathematical statistics principles underlying statistical analyses in the fields of economics, business, and econometrics. The selection of topics is designed to provide students with a substantial conceptual foundation from which to achieve a thorough and mature understanding of statistical applications within the fields. The examples and problems are intended to show the wide applicability of statistics in the fields, with the large majority having specific business and economic contexts. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. ... Read more

Customer Reviews (6)

Great book, terrible printing
I just got the book a few weeks ago, and read some chapters. I would say that it is a great textbook on mathematical statistics which best fit as a textbook for an advanced course in mathematical statistics.

Some notes:
1) The asymptotic statistic chapter is very thorough.
2) It is not too much oriented towards economics (which is fine with me).
3) When theorems are not explicitly proved, a specific reference is given.
4) Many examples are given for GLM.

The reason that I bought it was that I could not find it in the university library. In fact, I read somewhere that it is out of print. Unfortunately, the copy I got has very bad printing (I swear that it looks as if they scanned the original book) and after a day it has disconnected from the hard cover. VERY BAD PRODUCTION!

Excellent Prep for Econ PhD
I bought this book because I was worried about starting an Econ PhD program without any experience in mathematical statistics. I am so incredibly pleased with my purchase. The author clearly lays out the axiomatic theory of probability and then continues to mathematical statistics, using many examples drawn entirely from economics. It is so helpful to see the connection to the material where I will actually be using probability. I'm so glad that I bought this book instead of a more general approach to probability and statistics.

Fantastic Book
This is an excellent book on mathematical statistics.Although the treatment is less mathematical than if it were written for engineers or mathematicians, the gist of the topics is clearly written and the format is easy to follow.It covers all major topics needed for a firm understanding of mathematical statistics, and is a good background to econometric theory.I must admit that I did not know who the author was prior to reading this book, but he is one of the more decent writers out there who uses the right amount of mathematics to get the point across.

outstanding textbook
One of the most beautifully written books in mathematical statistics with the right mix of rigor and simplicity. A must read book before jumping into econometrics.

Reader's delight
One of the most beautifully written books in mathematical statistics with the right amount of rigor and simplicity. A new generation book, a book for the 21st century economists,statisticians,business professionals. A mustread book before jumping into econometrics. ... Read more

Product Description
Praise for the First Edition

"An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus."
–Journal of the American Statistical Association

"This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy."
–Journal of the Operational Research Society

Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, André Khuri has reexamined his popular work and substantially expanded it to provide the most up-to-date and comprehensive coverage of the subject.

Retaining the original’s much-appreciated application-oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on:

• Basic topological concepts
• Orthogonal polynomials
• Fourier series
• Approximation of integrals
• Solutions to selected exercises

The volume’s user-friendly text is notable for its end-of-chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought-out solutions to exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource. ... Read more

Product Description
A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.


* Contains 25% new material
* Includes the most complete coverage of sufficiency
* Transformation of Random Vectors
* Sufficiency / Completeness / Exponential Families
* Order Statistics
* Elements of Nonparametric Density Estimation
* Analysis of Variance (ANOVA)
* Regression Analysis
* Linear Models ... Read more

Customer Reviews (3)

A decent text.
This is not a bad text to have in your library but it is a bit rough to follow.Some of the proofs are left out which might otherwise help out understanding.

cryptic, brief, leaves you wanting much more...
Unfortunately, this book was used as the textbook in a mathematical statistics class taught by the author at UC Davis, which I was enrolled in.I found the book to be extremely brief, cryptic, and failed to even begin to explain the subject at hand in any kind of depth.I am an engineering student and am accustomed to technical material.This is the kind of textbook that gives the sciences a bad image.Being rigorous does not imply that you must be cryptic.Statistics is an exciting subject and this book utterly fails to inspire, explain, and enlighten.

An excellent calculus-based statistics book.
This is one of the best math books I have ever read. It's level of difficulty falls somewhere between a lower-division and graduate course on statistics. I would recommend it for anyone who wants to understand themathematical principles leading to the great results that are typicallyspoonfed to Freshman stat. students. Roughly 40% of the book reviewsprobability, while the remaining text draws on these chapters whiledeveloping the mathematical theory of statistics. I was pleased with thenumerous concrete examples, and the numerous excercises which for the mostpart were similar to the examples. From reading this book I gained anappreciation for the subject, and it's place in mathematics. I now considerstatistics as one of the well-developed crown jewels of mathematics, asopposed to my previous view of it as a superficial branch of math thatlacked rigor. ... Read more

Product Description
Understandable Statistics is a thorough, yet approachable statistics text. Designed to help students overcome their apprehension about statistics, the text provides guidance and informal advice showing students the links between statistics and their everyday lives. To reinforce this approach, the book integrates real-life data selected from a variety of sources including journals, periodicals, newspapers and the Internet. The use of graphing calculators, Excel, Minitab and SPSS is covered, but not required. A set of technology resources accompanying the Eighth Edition, designed to provide reinforcement for struggling students, includes a market-leading video and DVD series, interactive lessons, and simulations. ... Read more

Customer Reviews (12)

Satisfied.
Satisfied with my review. I received my order quicker than expected... within about 3 days, which was great because I was in my second week of classes and really needed the book. Thank You!

Understandable Statistics 8th edition
This book came in very nice condition I was happy with the price and purchase. I would buy again from seller.

understandable?
If you're looking for a book that will teach you the basic statistical tests (various t tests, linear regression, ANOVA, chi)and it's you're first contact with statistics then in my judgement this is an excellent book. In comparison to other books on stats the book even dives into basic probability theory in order to give a solid ground for understanding the tests - this was one of the reason for my purchase of this book. Furthermore the book ends with some basic non-parametric tests which other books in my experience often leave to more specialised litterature. At all times the book supplies a lot of examples, thorough explanation and problem sections with solutions - this makes the book somewhat slow at times, but for beginners without a math degree this is in my judgement a good buy. And I'm not just saying that because I bought it used for 3$ :)

stat book
It's very easy to understand and they give you examples all along the way. My favorite math book yet.

Great review book
I run into some problems related to statistics and needed a review course. I had 6 or seven different books left by other family members, who studied statistics in a variety of colleges. I went through all of them and this is the best: it skips most of the math but manages to explain all the relevant points. There is a plenty of examples and guided exercises. Authors dug up really interesting statistical problems from real life and inserted references to a variety of interesting books about all facets of reality. The problems to solve are fun and touch on everything in the book.
This is not the book I'd choose to study statistics in depth, but it's great for what I wanted to do. I managed to read the whole book on my own in 4 weeks and that wasn't all that difficult. ... Read more

Product Description
Appropriate for a one-term introductory statistics course, this text introduces statistical concepts and methods from a predominantly Bayesian perspective.It covers standard topics taking the Bayesian view that subjectivity is inevitable in science and that different conclusions from the same study are normal and stresses the advantages of this approach in scientific inference.It presents statistics as a means of integrating data into the scientific process and stresses data analysis and experimental design ideas early. ... Read more

Customer Reviews (5)

The right place to start
Excellent for self study. I was able to follow everything up to chapter 11 completely unaided.

nice elementary text on Bayesian methods
This is an excellent introductory text designed for a first course in statistics. It covers all the topics that are typically in a first course. However, all other texts at this level take the frequentist approach to inference. A few may have sections that introduce Bayesian ideas but the Bayesian approach is a paradigm for statistical inference and as such the approach should be incorporated in all statistical topics. Berry shows that this can be done without the student having to know calculus. To understand Bayesian methods the student mainly has to know that posterior probability = likelihood x prior probability. Berry provides a good list of references for those who want to pursue more advanced topics.
This book is unique. It demonstrate that statistics can be taught from the Bayesian approach in the very beginnning. This is much like what Noether did when he wrote an introductory text in statistics taking a strict nonparametric approach.

The text is loaded with exercises and the exposition is very clear. There are many useful and entertaining diagrams. Many examples are taken from real medical problems. Medicine is an area in which Berry has done a great deal of consulting and his experience shows in his examples. This should be the text to turn to if you want an introduction to the subject. If you know the basics and want more advanced treatment go to the references mentioned in Berry's preface.

Excellent introduction.
This is a truly clear and thoughtful introduction to Bayesian statistics.Nothing is taken for granted as the author leads you through examples and concepts. This was my first introduction to Bayesian statistics, and Berry makes it seem so much more reasonable and closer to real research/real life than the artifice involved in other approaches.

An excellent introduction
This book completely fulfills its goals, one of which is not to be a definitive reference book. It provides a friendly, entertaining introduction into statistics from a Bayesian perspective.

Introduction book
It is not too useful for people beyond college level. Not as a reference book. ... Read more

Product Description
MATHEMATICAL STATISTICS by S. S. WILKS.PREFACE: Most of the mathematical theory of statistics In Its present state has been developed during the past twenty years. Because of the variety of scientific fields In which statistical problems have arisen, the original contributions to this branch of applied mathematics are widely scattered In scientific literature. Most of the theory still exists only In original form. During the past few years the author has conducted a two-semester course at Princeton University for advanced undergraduates and beginning graduate students in which an attempt has been made to give the students an Introduction to the more recent develop ments in the mathematical theory of statistics. The subject matter for this course has been gleaned, for the most part, from periodical literature. Since it is impossible to cover in detail any large portion of this literature in two semesters, the course has been held primarily to the basic mathematics of the material, with just enough problems and examples for illustrative and examination purposes. Except for Chapter XI, the contents or the present set of notes constitute the basic subject matter which this course was designed to cover. Some of the material in the authors Statistical Inference 1937 has been revised and Included. In writing up the notes an attempt has been made to be as brief and concise as possible and to keep to the mathematics with a minimum of excursions into applied mathematical statistics problems. An important topic which has been omitted is that of characteristic functions of random variables, which, when used in Fourier Inversions, provide a direct and powerful method of determining certain sampling distributions and other random variable distribu tions. However, moment generating functions are used they are more easily understood by students at this level and are almost as useful as characteristic functions as far as actual applications to mathematical statistics are concerned. Many specialized topics are omitted, such as intraclass, tetrachoric and other specialized correlation problems, aeml-lnvariants, renewal theory, the Behrens - Fisher problem, special transformations of population parameters and random variables, sampling from Poisson populations, etc. It is the experience of the author that an effective way for handling many of these specialized topics is to formulate them as problems for the students. If and when the present notes are revised and issued in permanent form, such problems will be Inserted at the ends of sections and chapters. In the meantime, criticisms, suggestions, and notices of errors will be gratefully received from readers. Finally, the author wishes to express his indebtedness to Dr. Henry Scheffe, Mr. T. W. Anderson, Jr. and Mr. D. F. Votaw, Jr. for their generous assistance in pre paring these notes. Most of the sections in the first seven chapters and several sections in ChapteSX and XI were prepared by these men, particularly the first two. Thanks are due Mrs. W. M. Weber for her painstaking preparation of the manuscript for lithoprinting. S. S. Wilks. Contents include: CHAPTER I, INTRODUCTION 1 CHAPTER II. DISTRIBUTION FUNCTIONS 52.1 Cumulative Distribution Functions 5 2.11 IMivariate Case 5 2.12 Blva rlate Case 8 52.13 k-Variate Case 11 2.2 Marginal Distributions 12 52.3 Statistical Independence 13 52.1 Conditional Probability 15 52.5 The Stleltjes Integral 17 52.51 Univarlate Case 17 52.52 Blvarlate Case 20 52.53 k-Variate Case 21 52.6 Transformation of Variables 23 2.61 Unlvariate Case 2k 2.62 Blvarlate Case 2k 52.63 k-Vtetrlate Case 28 52.7 Mean Value 29 52.71 Univarlate Case Tchebychef f f s Inequality 30 52.72 Bivariate Case 31 52.73 k-Variate Case 32 52.71 Mean and Variance of a Linear Combination of Bandom Variables 33 52... ... Read more

Customer Reviews (2)

great and extensive introductory text
It is very difficult to have an introductory text do justice to the theory of probability and statistics, especially in a first course. Although the emphasis is greater on statistics, Rohatgi does a great job of covering both topics extensively and that is why the book had to be this thick!

Areference statistic book
If you want to understand the Probability Theory, this book is the best instrument that I know for this target. It deals with probabilities without using complex numbers: the characteristic function doesn`t appear in it:the autor used the moment generating function instead. In this book you canfind the most important things about the normal distribution and othercontinuous distribution related with it: the Student t-distribution, thechi-square and the Snedecor's F-distribution, the Cauchy distribution...For every important result you may find a lot of examples where you canapply it or counterexamples which shows you where you can't. It's a strongbook to know the estimation of a real parameter or to learn how to teststatistical hypotheses. It handles too with nonparametric inference. Youcan find also random vectors in this book, but you may find better books ifyou're interesting in this matter. ... Read more

Product Description

Study faster, learn better-and get top grades with Schaum's Outlines

Customer Reviews (16)

very condensed
This book and the way it's advertised make it seem like an idiot's guide to Stats. However, it's not. It's actually pretty dense for that. It is a great supplement to a Stats class. It cuts through a lot of the nonsense and verbiage of many stats texts. I'd suggest using this to supplement the class (after lectures etc). It's also great to refresh yourself on basic stats and probability concepts once you've taken a course. I just wish it had more diagrams and pictures of the various distributions.

Love Schaum's!Have Used Them Since the Early 70s!
Simply the best subject outlines with the most worked out problems - and problems with answers!

The most comphrehensive book on Statistics
Whether you are in senior years of your undergrad or a initial years of your PhD, you would be wasting your time learning stats from any book otherthan this. Very to-the-point explanation of essential concepts, excellent worked out examples, and quick review of the theory of stats - all packed in one neat book for great price. I would not be able to do my PhD studies without Schaum.

An excellent introduction to statistics
I salute, with great joy, the McGraw-Hill initiative for re-publishing this classic of Schaum's Outline of Theory and Problems in Statistics in a new and revised edition. The late Professor Murray Spiegel -a scholar, who wrote 14 books (!!) on various topics in mathematics-, profoundly marked my college days. I perfectly recall his keen sense of practicality. Vector Analysis and Complex Variables, among Spiegel's most accomplished endeavours, were (and still are) my bedside books. His pedagogical skills are also present in his Statistics. Professor Larry Stephens (Spiegel's co-author), who cleverly preserved the backbones of the book, carefully updated the material to allow for the deep technological changes undergone by contemporary societies since the first edition appeared in 1961. With a profusion of problems solved, this fourth edition that includes "...130 new figures, output from five computer software packages representative of the hundreds or perhaps thousands of computer software packages that are in use in statistics..." and a new chapter (Statistical Process Control and Process Capability) is here to stay. I particularly appreciated the pedagogical thread in the presentation of the subject: the authors introduce the essential of statistics in an easy-to-follow, topic-by-topic format. By revising college algebra topics (chapter 1; Variables and Graphs, chapter 6 ; Elementary Probability Theory) students are invited to learn step by step statistical distributions, elementary sampling theory, analysis of variance and the like of a discipline whose fields of application are as vast as the human brain can reach. I liked the book very much indeed.

excellent book
you cant beat it, lots of examples, with full solutions, plus lots of practice problems with all the solutions even and odd, for [...] bucks you cant go wrong. ... Read more

Product Description

In this 3rd edition revised text, master expositor Sheldon Ross has produced a unique work in introductory statistics. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, and an explanation of intuition and ideas behind the statistical methods. Concepts are motivated, illustrated and explained in a way that attempts to increase one's intuition. To quote from the preface, "It is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data."

Customer Reviews (2)

Clear explanations but poorly edited
I bought this book for a university level statistics course. While the book has been helpful, I have been troubled by the vast number of editorial mistakes in the sample problems - wrong answers, incorrect data tables etc. Most textbooks have an error or two, but so far I have come across mistakes in every chapter.

Stats = Fun
With this excellently written, lively, and sometimes tear-jerking look into the basic principles of statistics, there is not a chance in hell your kids won't grown up to be rocket scientists. ... Read more

Product Description
This is the first half of a set of lecture notes with exercises - a text - for two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. ... Read more

Product Description
The best intermediate-level explanation of classical statistics on the market! From basic dice probabilities to modern regression analysis and correlation, Professor Bulmer provides explanations, graphs, charts, problems (with answers). Equal stress is given to theory and applications. The author assumes no previous knowledge of statistics or probability; only basic calculus is needed. Ideal college-level or supplementary text.
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Customer Reviews (21)

Book Review
Great statistics book for a graduate student. You may need some introductory statistics or some undergrad math classes to understand this text. Its advanced, and looks at several theories in detail. Makes a great reference and a guide to several statistical theories, sometimes advanced.

Statistics at a glance
Principles of statistics is not a new book (1967). Therefore, it include a modern approach if compared with that era. Actually, the major advantage in read this publication will be found in its simply structure. A student in physiotherapy or in nursing science or people who are interested in statistic should be recognize a lot of useful information after reading. This book could be the best way to learn the basic of statistic especially for the health professions. Also the ratio price/quality is really good. Student, after reading, they should be able to make inferential in their data set and finally understand this particular matter often not really simple.

Reads like a textbook and is just as vague
I am a very math oriented person. I like formulas to be laid out in front of me and I love looking at the steps that it took to solve a problem. What I always hated about textbooks is that they would skip steps throughout a problem. Once you're lost, you stay lost. I took some very high level statistic courses in college, was always kind of lost, and thought I would go through it again with hopefully a better book than what we had.

This book is even worse. Formulas are mentioned mid-paragraph and are not laid out in an "orderly" manner. There are no steps shown to how referenced example problem solutions were achieved. A formula will be mentioned, an example table will be displayed, a question will be posed, and the final answer is shown. This book is for those who already have a solid foundation. New comers stay away!

Way overrated
Having read some great reviews for this book on Amazon, I went to the library to check the book out and was rather disappointed. The book is OK, but nothing to rave about. It uses rather archaic probabilistic language, not very precise in the statements and sometimes plainly boring. Moreover a good half of it contains a less than perfect intro to probability. All in all, not a bad book, but probably not worth buying.

Unlocks the mystery behind the equations
The positive reviews for this book seem to be written by people with a previous background in statistics and/or strong math skills.Furthermore, they want to know the why behind every equation.I mostly fall into this category.

The negative reviews come from people who use this as their introduction to statistics, and who probably don't have a strong grasp of calculus or perhaps higher level math in general.

In my opinion this book offers something that no other statistics book has: clear derivations of all the fundamental and important equations and distributions in statistics; followed by lucid explanations.In other words this book unravels the mystery behind the equations.If you've thought about a statistics equation a lot and wondered, WHY? Then this is the book to read.

Here are 4 questions I had that Bulmer answered:
1) Why is the mean more commonly used than the median (and in which cases is the median better)? p.51-54
2) As a measure of variability why use a root-mean-square procedure (i.e. accepted def. of std deviation ) instead of mean deviation (i.e. take absolute value of deviations)? p.54-59
3) What is the logical error in the gambler's fallacy? p.87-88 (Note: many statistics books treat this, but I've found Bulmer's book to give the most satisfying answer.)
4) Why does the standard deviation of a sample have the n-1 term in the denominator instead of the n term like the stdev of the population? p.129-130

(Note that he answers questions 1, 2, and 4 more than once, but the pages listed are the first time the answer appears.)

Thus, I strongly recommend buying and reading this book if, like me, you have a burning desire to know why the equations are the way they are.I would recommend a different book, say Statistics by Freedman, if you're either new to statistics or you don't have a great handle on math (i.e. proofs, calculus, etc.).

Note that Statistics by Freedman is an excellent introductory text with a plethora of examples and will not take you down the terrible path of memorizing formulas that you don't understand.Rather it seeks to give a conceptual understanding of statistics without delving too deeply into the underlying math.

Finally, I gave Bulmer's book 4 stars rather than 5 because Bulmer often derives equations that I'm not interested in. ... Read more

Product Description

The revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), coverage of residual analysis in linear models, and many examples using real data. Calculus is assumed as a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus.

Customer Reviews (25)

too much proof, too little application, hard to read!!!!
I used this book for my statistics class.The author makes simple concept hard to understand.It contains pages of proofs to a simple formula.I tried to follow the proof, but it was confusing.The proofs were not basic and intuitive calculus.It did not help me do well in the class either.I almost forgot what I was trying to prove when I followed through.

The book does not explain how to use the formulas.So, the problem sets are hard, because you are not sure how to apply the formulas.

A lot of the later examples are based on the result of the earlier ones.So, it can be very hard to pick up from the middle of the book.It also happens in the problem set, the result from question 1 is needed to complete question four.

Solid text for the study of probability and statistics for math majors
An earlier edition of this book was the text when I took my first course in probability and statistics. Now that I teach math and computer science at a small college I am always on the lookout for a new text and so I examined this book within that context. The coverage is at a high mathematical level; there are many theorems with proof. However, there are also many worked examples that demonstrate how the theorems are applied. The quality of the exposition is such that it is very readable for those who have gone through a three-semester calculus sequence.
The chapters are:

*) Introduction to probability
*) Conditional probability
*) Random variables and distributions
*) Expectation
*) Special distributions
*) Estimation
*) Sampling distributions of estimators
*) Testing hypotheses
*) Categorical data and nonparamentric methods
*) Linear statistical models
*) Simulation

A large set of problems appears at the end of each chapter and solutions to the odd-numbered ones are included in an appendix.
The high level of readability that I appreciated so much when I learned from an earlier edition has been maintained through this one. I can strongly recommend this book as a text for upper level courses in probability and statistics.

Fantastic Into Probability and Stats Book
This book is a fantastic introduction to probability and statistics.It is clear and presents the material with lots of accompanying intuitive explanations.The book also has lots of great examples that clarify the theory and show how the theory can be applied.This book has a strong focus on Bayesian methods, so it is a good place to start if you are trying to learn Bayesian statistics.I love this book.

The truth about this book.99% of other great reviews are bogus.
This book was not written for students.It was written so that the author can gain respect from his from his academic peers.The explanations are absolutely horrible.It purposely explains simple concepts in overly verbose, complicated ways.The idea is to make the subject appear as complicated as possible when it doesn't need to be.It reads like those academic papers that are purposely written in overly complicated language so that nobody understands what the author is talking about except the author himself.The idea is to impress his academic circle by showing that he did a "complicated" analysis.

When are these people going to learn that "simplicity is the ultimate sophistication" - Da Vinci?

Here's an example.Do you know what's a percentile?Think about your SAT or GRE score report.80th percentile means 80% of the people scored lower than you.90th percentile means 90% of the people scored lower than you.Simple, right?This book introduces the concept like this:

"The d.f. of a random variable X gives us the probability that X<=x for all real numbers x.It is often the case that we choose a probability, like 1/2, and we want to know where in the distribution of X we can find that probability.For example, suppose that X is the amount of rain that will fall tomorrow and we want to place an even-money bet on X as follows.If X<=x0, we win one dollar and if X>x0 we lose one dollar.In order to make this bet fair, we need Pr(X<=xo)=Pr(X>x0)=1/2.We could use all the real numbers x trying to find one such that F(x)=1/2, and then we could let x0 equal the value we found.If F is a one-to-one function, then F has an inverse F^-1 and x0=F^-1(1/2)." - P.114

Lol! If you want to learn like this, go ahead and buy this book.I'll give this book two stars because there are probably a few souls out there who actually do prefer to learn like this.

Best intro reference for graduate students
This is by far the best graduate text for basic probability and statistics that is currently made.It even nicely incorporates Bayesian material in a completely relevant way.No, it is probably too complex and abstract for complete beginners in probability as many of the reviewers here have suggested.For anyone with even just a basic background in statistics or probability, however, it is perfect.It is straightforward, comprehensive and most importantly highly readable.There is no comparison to other probability/statistics texts I own--if you are pursuing any sort of graduate level study in statistics or basic probability this the textbook to own and reference. ... Read more

Customer Reviews (2)

Excellent Introduction to Mathematical Statistics
Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)


I read the third edition when it was first published.I was in school; I used it in an undergraduate class.Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published.The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen.The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."


Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))


Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)


The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))


Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* (Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics))


I've enjoyed this book since I first read it in 1971.The new edition is every bit as practical and enjoyable as the older editions.I recommend it to others with no reservations.

Excellent Introduction to Mathematical Statistics
Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)


I read the third edition when it was first published.I was in school; I used it in an undergraduate class.Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published.The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen.The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."


Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))


Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)


The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))


Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* (Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics))


I've enjoyed this book since I first read it in 1971.The new edition is every bit as practical and enjoyable as the older editions.I recommend it to others with no reservations.


... Read more