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E-raamat: Modern Mathematical Statistics with Applications

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  • Sari: Springer Texts in Statistics
  • Ilmumisaeg: 29-Apr-2021
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030551568
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  • Formaat: PDF+DRM
  • Sari: Springer Texts in Statistics
  • Ilmumisaeg: 29-Apr-2021
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030551568
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Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. The text illustrates statistical concepts and methods through careful explanations and real-data applications.



This 3rd edition of Modern Mathematical Statistics with Applications tries to strike a balance between mathematical foundations and statistical practice.  The book provides a clear and current exposition of statistical concepts and methodology, including many examples and exercises based on real data gleaned from publicly available sources. Here is a small but representative selection of scenarios for our examples and exercises based on information in recent articles:
  • Use of the “Big Mac index” by the publication The Economist as a humorous way to compare product costs across nations
  • Visualizing how the concentration of lead levels in cartridges varies for each of five brands of e-cigarettes
  • Describing the distribution of grip size among surgeons and how it impacts their ability to use a particular brand of surgical stapler
  • Estimating the true average odometer reading of used Porsche Boxsters listed for sale on www.cars.com
  • Comparing head acceleration after impact when wearing a football helmet with acceleration without a helmet
  • Investigating the relationship between body mass index and foot load while running
The main focus of the book is on presenting and illustrating methods of inferential statistics used by investigators in a wide variety of disciplines, from actuarial science all the way to zoology.  It begins with a chapter on descriptive statistics that immediately exposes the reader to the analysis of real data.  The next six chapters develop the probability material that facilitates the transition from simply describing data to drawing formal conclusions based on inferential methodology.  Point estimation, the use of statistical intervals, and hypothesis testing are the topics of the first three inferential chapters.  The remainder of the book explores the use of these methods in a variety of more complex settings.

This edition includes many new examples and exercises as well as an introduction to the simulation of events and probability distributions.  There are more than 1300 exercises in the book, ranging from very straightforward to reasonably challenging.  Many sections have been rewritten with the goal of streamlining and providing a more accessible exposition.  Output from the most common statistical software packages is included wherever appropriate (a feature absent from virtually all other mathematical statistics textbooks).  The authors hope that their enthusiasm for the theory and applicability of statistics to real world problems will encourage students to pursue more training in the discipline.

Arvustused

The textbook Modern Mathematical Statistics with Applications can be recommended for applied mathematics and statistics majors as well as prospective scientists, business, social and medical science majors interested in the applying modern statistical methods for their disciplines. (Maria Ivanchuk, ISCB News, iscb.info, June, 2022)

1 Overview and Descriptive Statistics
1(48)
1.1 The Language of Statistics
1(8)
1.2 Graphical Methods in Descriptive Statistics
9(16)
1.3 Measures of Center
25(7)
1.4 Measures of Variability
32(17)
Supplementary Exercises
43(6)
2 Probability
49(62)
2.1 Sample Spaces and Events
49(6)
2.2 Axioms, Interpretations, and Properties of Probability
55(11)
2.3 Counting Methods
66(9)
2.4 Conditional Probability
75(12)
2.5 Independence
87(7)
2.6 Simulation of Random Events
94(17)
Supplementary Exercises
103(8)
3 Discrete Random Variables and Probability Distributions
111(78)
3.1 Random Variables
111(4)
3.2 Probability Distributions for Discrete Random Variables
115(11)
3.3 Expected Values of Discrete Random Variables
126(11)
3.4 Moments and Moment Generating Functions
137(7)
3.5 The Binomial Probability Distribution
144(12)
3.6 The Poisson Probability Distribution
156(8)
3.7 Other Discrete Distributions
164(9)
3.8 Simulation of Discrete Random Variables
173(16)
Supplementary Exercises
182(7)
4 Continuous Random Variables and Probability Distributions
189(88)
4.1 Probability Density Functions and Cumulative Distribution Functions
189(14)
4.2 Expected Values and Moment Generating Functions
203(10)
4.3 The Normal Distribution
213(17)
4.4 The Gamma Distribution and Its Relatives
230(9)
4.5 Other Continuous Distributions
239(8)
4.6 Probability Plots
247(11)
4.7 Transformations of a Random Variable
258(5)
4.8 Simulation of Continuous Random Variables
263(14)
Supplementary Exercises
269(8)
5 Joint Probability Distributions and Their Applications
277(80)
5.1 Jointly Distributed Random Variables
277(17)
5.2 Expected Values, Covariance, and Correlation
294(9)
5.3 Linear Combinations
303(14)
5.4 Conditional Distributions and Conditional Expectation
317(13)
5.5 The Bivariate Normal Distribution
330(6)
5.6 Transformations of Multiple Random Variables
336(6)
5.7 Order Statistics
342(15)
Supplementary Exercises
350(7)
6 Statistics and Sampling Distributions
357(40)
6.1 Statistics and Their Distributions
357(11)
6.2 The Distribution of Sample Totals, Means, and Proportions
368(12)
6.3 The Χ2, t and F Distributions
380(8)
6.4 Distributions Based on Normal Random Samples
388(9)
Supplementary Exercises
393(2)
Appendix: Proof of the Central Limit Theorem
395(2)
7 Point Estimation
397(54)
7.1 Concepts and Criteria for Point Estimation
397(19)
7.2 The Methods of Moments and Maximum Likelihood
416(12)
7.3 Sufficiency
428(8)
7.4 Information and Efficiency
436(15)
Supplementary Exercises
445(6)
8 Statistical Intervals Based on a Single Sample
451(50)
8.1 Basic Properties of Confidence Intervals
452(11)
8.2 The One-Sample t Interval and Its Relatives
463(12)
8.3 Intervals for a Population Proportion
475(6)
8.4 Confidence Intervals for the Population Variance and Standard Deviation
481(3)
8.5 Bootstrap Confidence Intervals
484(17)
Supplementary Exercises
494(7)
9 Tests of Hypotheses Based on a Single Sample
501(64)
9.1 Hypotheses and Test Procedures
501(11)
9.2 Tests About a Population Mean
512(14)
9.3 Tests About a Population Proportion
526(6)
9.4 P-Values
532(10)
9.5 The Neyman-Pearson Lemma and Likelihood Ratio Tectc
542(11)
9.6 Further Aspects of Hypothesis Testing
553(12)
Supplementary Exercises
560(5)
10 Inferences Based on Two Samples
565(74)
10.1 The Two-Sample z Confidence Interval and Test
565(10)
10.2 The Two-Sample t Confidence Interval and Test
575(16)
10.3 Analysis of Paired Data
591(11)
10.4 Inferences About Two Population Proportions
602(9)
10.5 Inferences About Two Population Variances
611(6)
10.6 Inferences Using the Bootstrap and Permutation Methods
617(22)
Supplementary Exercises
630(9)
11 The Analysis of Variance
639(64)
11.1 Single-Factor ANOVA
640(13)
11.2 Multiple Comparisons in ANOVA
653(9)
11.3 More on Single-Factor ANOVA
662(10)
11.4 Two-Factor ANOVA without Replication
672(15)
11.5 Two-Factor ANOVA with Replication
687(16)
Supplementary Exercises
699(4)
12 Regression and Correlation
703(120)
12.1 The Simple Linear Regression Model
704(9)
12.2 Estimating Model Parameters
713(14)
12.3 Inferences About the Regression Coefficient β1
727(10)
12.4 Inferences for the (Mean) Response
737(8)
12.5 Correlation
745(12)
12.6 Investigating Model Adequacy: Residual Analysis
757(10)
12.7 Multiple Regression Analysis
767(16)
12.8 Quadratic, Interaction, and Indicator Terms
783(12)
12.9 Regression with Matrices
795(11)
12.10 Logistic Regression
806(17)
Supplementary Exercises
817(6)
13 Cbi-Squared Tests
823(32)
13.1 Goodness-of-Fit Tests
823(17)
13.2 Two-Way Contingency Tables
840(15)
Supplementary Exercises
851(4)
14 Nonparametric Methods
855(34)
14.1 Exact Inference for Population Quantiles
855(6)
14.2 One-Sample Rank-Based Inference
861(10)
14.3 Two-Sample Rank-Based Inference
871(8)
14.4 Nonparametric ANOVA
879(10)
Supplementary Exercises
886(3)
15 Introduction to Bayesian Estimation
889(14)
15.1 Prior and Posterior Distributions
889(7)
15.2 Bayesian Point and Interval Estimation
896(7)
Appendix 903(23)
Answers to Odd-Numbered Exercises 926(37)
References 963(2)
Index 965
Jay L. Devore received a B.S. in Engineering Science from the University of California, Berkeley, and a Ph.D. in Statistics from Stanford University. He previously taught at the University of Florida and Oberlin College, and has had visiting positions at Stanford, Harvard, the University of Washington, New York University, and Columbia. He has been at California Polytechnic State University, San Luis Obispo, since 1977, where he was chair of the Department of Statistics for seven years and recently achieved the exalted status of Professor Emeritus.

Jay has previously authored or coauthored ve other books, including Probability and Statistics for Engineering and the Sciences, which won a McGuffey Longevity Award from the Text and Academic Authors Association for demonstrated excellence over time. He is a Fellow of the American Statistical Association, has been an associate editor for both the Journal of the American Statistical Association and The American Statistician, and received the Distinguished Teaching Award from Cal Poly in 1991. His recreational interests include reading, playing tennis, traveling, and cooking and eating good food.

Kenneth N. Berk has a B.S. in Physics from Carnegie Tech (now Carnegie Mellon) and a Ph.D. in Mathematics from the University of Minnesota. He is Professor Emeritus of Mathematics at Illinois State University and a Fellow of the American Statistical As­sociation. He founded the Software Reviews section of The American Statistician and edited it for six years. He served as secretary/treasurer, program chair, and chair of the Statistical Computing Section of the American Statistical Association, and he twice co-chaired the Interface Symposium, the main annual meeting in statistical computing. His published work includes papers on time series, statistical computing, regression analysis, and statistical graphics, as well as the book Data Analysis with Microsoft Excel (with Patrick Carey).

Matthew A. Carlton is Professor of Statistics at California Polytechnic State University, San Luis Obispo, where he joined the faculty in 1999. He received a B.A. in Mathematics from the University of California, Berkeley and a Ph.D. in Mathematics from the University of California, Los Angeles, with an emphasis on pure and applied probability; his thesis research involved applications of the Poisson-Dirichlet random process. Matt has published papers in the Journal of Applied Probability, Human Biology, Journal of Statistics Education, and The American Statistician. He was also the lead content adviser for the Statistically Speaking video series, designed for community college statistics courses, and he has published a variety of educational materials for high school statistics teachers. Matt was responsible for developing both the applied probability course and the probability and random processes course at Cal Poly, which in turn inspired him to get involved in writing this text. His professional research focus involves applications of probability to genetics and engineering. Personal interests include travel, good wine, and college sports.