Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without emphasizing contemporary statistical practice. MODERN MATHEMATICAL STATISTICS WITH APPLICATIONS strikes a balance between mathematical foundations and statistical practice. Accomplished authors Jay Devore and Ken Berk first engage students with real-life problems and scenarios and then provide them with both foundational context and theory. This book follows the spirit of the Committee on the Undergraduate Program in Mathematics (CUPM) recommendation that every math student should study statistics and probability with an emphasis on data analysis.
Jay Devore is Professor Emeritus of Statistics at California Polytechnic State University. He earned his undergraduate degree in Engineering Science from the University of California at Berkeley, spent a year at the University of Sheffield in England, and finished his Ph.D. in statistics at Stanford University. Jay previously taught at the University of Florida and at Oberlin College and has had visiting appointments at Stanford, Harvard, the University of Washington, New York University, and Columbia University. From 1998 to 2006, he served as Chair of the Statistics Department. In addition to this book, Jay has written several widely used engineering statistics texts and a book in applied mathematical statistics. He recently coauthored a text in probability and stochastic processes. He is the recipient of a distinguished teaching award from Cal Poly, is a Fellow of the American Statistical Association , and has served several terms as an Associate Editor of the "Journal of the American Statistical Association." In his spare time, he enjoys reading, cooking and eating good food, tennis, and travel to faraway places. He is especially proud of his wife, Carol, a retired elementary school teacher, his daughter Allison, who has held several high-level positions in nonprofit organizations in Boston and New York City, and his daughter Teresa, an ESL teacher in New York City.
Ken Berk has a BS in Physics from Carnegie Tech (now Carnegie Mellon) and a PhD in Mathematics from 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 and the book Data Analysis with Microsoft Excel (with Patrick Carey).
1.OVERVIEW AND DESCRIPTIVE STATISTICS. Introduction. Populations, Samples, and Processes. Pictorial and Tabular Methods in Descriptive Statistics. Measures of Location. Measures of Variability. 2.PROBABILITY. Introduction. Sample Spaces and Events. Axioms, Interpretations, and Properties of Probability. Counting Techniques. Conditional Probability. Independence. 3.DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Random Variables. Probability Distributions for Discrete Random Variables. Expected Values of Discrete Random Variables. Moments and Moment Generating Functions. The Binomial Probability Distribution. The Hypergeometric and Negative Binomial Distributions. The Poisson Probability Distribution. 4.CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Probability Density Functions and Cumulative Distribution Functions. Expected Values and Moment Generating Functions. The Normal Distribution. The Gamma Distribution and Its Relatives. Other Continuous Distributions. Probability Plots. Transformations of a Random Variable. 5.JOINT PROBABILITY DISTRIBUTIONS. Introduction. Jointly Distributed Random Variables. Expected Values, Covariance, and Correlation. Conditional Distributions. Transformations of Random Variables. Order Statistics. 6.STATISTICS AND SAMPLING DISTRIBUTIONS. Introduction. Statistics and Their Distributions. The Distribution of the Sample Mean. The Distribution of a Linear Combination. Distributions Based on a Normal Random Sample. Appendix. 7.POINT ESTIMATION. Introduction. Some General Concepts of Point Estimation. Methods of Point Estimation. Sufficiency. Information and Efficiency. 8.STATISTICAL INTERVALS BASED ON A SINGLE SAMPLE. Introduction. Basic Properties of Confidence Intervals. Large-Sample Confidence Intervals for a Population Mean and Proportion. Intervals Based on a Normal Population Distribution. Confidence Intervals for the Variance and Standard Deviation of a Normal Population. Bootstrap Confidence Intervals. 9.TESTS OF HYPOTHESES BASED ON A SINGLE SAMPLE. Introduction. Hypotheses and Test Procedures. Tests About a Population Mean. Tests Concerning a Population Proportion. P-Values. Some Comments on Selecting a Test Procedure. 10.INFERENCES BASED ON TWO SAMPLES. Introduction. z Tests and Confidence Intervals for a Difference between Two Population Means. The Two-Sample t Test and Confidence Interval. Analysis of Paired Data. Inferences about Two Population Proportions. Inferences about Two Population Variances. Comparisons Using the Bootstrap and Permutation Methods. 11.THE ANALYSIS OF VARIANCE. Introduction. Single-Factor ANOVA. Multiple Comparisons in ANOVA. More on Single-Factor ANOVA. Two-Factor ANOVA with Kij = 1. Two-Factor ANOVA with Kij > 1. 12.REGRESSION AND CORRELATION. Introduction. The Simple Linear and Logistic Regression Models. Estimating Model Parameters. Inferences about the Regression Coefficient ƒÒ1ƒ|ƒn Inferences Concerning ƒÝY„ªx*ƒn and the Prediction of Future Y Values. Correlation. Aptness of the Model and Model Checking. Multiple Regression Analysis. Regression with Matrices. 13.GOODNESS-OF-FIT TESTS AND CATEGORICAL DATA ANALYSIS. Introduction. Goodness-of-Fit Tests When Category Probabilities Are Completely Specified. Goodness-of-Fit Tests for Composite Hypotheses. Two-Way Contingency Tables. 14.ALTERNATIVE APPROACHES TO INFERENCE. Introduction. The Wilcoxon Signed-Rank Test. The Wilcoxon Rank-Sum Test. Distribution-Free Confidence Intervals. Bayesian Methods. Sequential Methods.