James H. Stapleton

Models for Probability and Statistical Inference

Theory and Applications

• Gebundenes Buch

Produktbeschreibung

This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers

Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.

Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression.

Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers

Produktdetails

• Wiley Series in Probability and Statistics
• Verlag: Wiley & Sons
• Artikelnr. des Verlages: 14507372000
• 1. Auflage
• Seitenzahl: 464
• Erscheinungstermin: 1. Dezember 2007
• Englisch
• Abmessung: 240mm x 161mm x 29mm
• Gewicht: 780g
• ISBN-13: 9780470073728
• ISBN-10: 0470073721
• Artikelnr.: 23117734

Autorenporträt

James H. Stapleton, PhD, has recently retired after forty-nine years as professor in the Department of Statistics and Probability at Michigan State University, including eight years as chairperson and almost twenty years as graduate director. Dr. Stapleton is the author of Linear Statistical Models (Wiley), and he received his PhD in mathematical statistics from Purdue University.

Inhaltsangabe

1. Probability Models. 1.1 Discrete Probability Models. 1.2 Conditional
Probability and Independence. 1.3 Random Variables. 1.4 Expectation. 1.5
The Variance. 1.6 Covariance and Correlation. 2. Special Discrete
Distributions. 2.1 The Binomial Distribution. 2.2 The Hypergeometric
Distribution. 2.3 The Geometric and Negative Binomial Distributions. 2.4
The Poisson Distribution. 3. Continuous Random Variables. 4.1 Continuous
RV's and Their Distributions. 4.2 Expected Values and Variances. 4.3
Transformations of Random Variables. 4.4Joint Densities. 4 Special
Continuous Distributions. 4.1 The Normal Distribution. 4.2 The Gamma
Distribution. 5. Conditional Distributions. 5.1 The Discrete Case. 5.2
Conditional Expectations for the Discrete Case. 5.3 Conditional Densities
and Expectations for Continuous RV's. 6. Limit Laws. 6.1 Moment Generating
Functions. 6.2 Convergence in Probability and in Distribution. 6.3 The
Central Limit Theorem. 6.4 The Delta-Method. 7. Estimation. 7.1 Point
Estimation. 7.2 The Method of Moments. 7.3 Maximum Likelihood. 7.4
Consistency. 7.5 The Omega-Method. 7.6 Confidence Intervals. 7.7 Fisher
Information, The Cramer-Rao Bound, and Asymptotic Normality of MLE's. 7.8
Sufficiency. 8. Testing Hypotheses. 8.1 Introduction. 8.2 The
Neyman-Pearson Lemma. 8.3 The Likelihood Ratio Test. 8.4 The p-Value and
the Relationship Between Tests of Hypotheses and Confidence Intervals. 9.
The Multivariate Normal, Chi-square, t, and F-Distributions. 9.1 The
Multivariate Normal Distribution. 9.2 The Central and Noncentral Chi-Square
Distributions. 9.3 Student's t-Distribution. 9.4 The F-Distribution. 10.3
Nonparametric Statistics. 10.1 The Wilcoxon Test and Estimator. 10.2 One
Sample Methods. 10.3 The Kolmogorov-Smirnov Tests. 11. Linear Models. 11.1
The Principle of Least Squares. 11.2 Linear Models. 11.3 F-Tests for H0.
11.4 Two-Way Analysis of Variance.. 12. Frequency Data. 12.1 Logistic
Regression. 12.2 Two-Way Frequency Tables. 12.3 Chi-Square Goodness of Fit
Tests. 13. Miscellaneous Topics. 13.1 Survival Analysis. 13.2
Bootstrapping. 13.3 Bayesian Statistics. 13.4 Sampling.

Rezensionen

"The whole first part of the book is very reader friendly and well written." ( CHOICE May 2008) "The prose throughout the book is clear and well aimed at first year master s student who is intelligent but not yet statistically sophisticated. Examples are clear and well chosen." ( Biometrics , March 2009)