Mathematical Statistics with Applications

Many students who do well in mathematics courses find it difficult to understand the concept of statistics. This book presents the material to help the students to approach problem solving in statistics in a logical manner. It provides a calculus based coverage of statistics and introduces methods of theoretical statistics and their applications.

Autorentext
Chris P. Tsokos is Distinguished University Professor of Mathematics and Statistics at the University of South Florida. Dr. Tsokos' research has extended into a variety of areas, including stochastic systems, statistical models, reliability analysis, ecological systems, operations research, time series, Bayesian analysis, and mathematical and statistical modelling of global warming, both parametric and nonparametric survival analysis, among others. He is the author of more than 400 research publications in these areas, including Random Integral Equations with Applications to Life Sciences and Engineering, Probability Distribution: An Introduction to Probability Theory with Applications, Mainstreams of Finite Mathematics with Applications, Probability with the Essential Analysis, Applied Probability Bayesian Statistical Methods with Applications to Reliability, and Mathematical Statistics with Applications, among others. Dr. Tsokos is the recipient of many distinguished awards and honors, including Fellow of the American Statistical Association, USF Distinguished Scholar Award, Sigma Xi Outstanding Research Award, USF Outstanding Undergraduate Teaching Award, USF Professional Excellence Award, Pi Mu Epsilon, election to the International Statistical Institute, Sigma Pi Sigma, USF Teaching Incentive Program, and several humanitarian and philanthropic recognitions and awards. He is also serves as Honorary Editor, Chief-Editor, Editor or Associate Editor for more than twelve academic research journals. Kandethody M. Ramachandran is Professor of Mathematics and Statistics at the University of South Florida. His research interests are concentrated in the areas of applied probability, statistics, machine learning, and generative AI. His research publications span a variety of areas such as control of heavy traffic queues, stochastic delay systems, machine learning methods applied to game theory, finance, cyber security, health sciences, and other emerging areas. He is also co-author of three books. He is the founding director of the Interdisciplinary Data Sciences Consortium (IDSC). He is extensively involved in activities to improve statistics and mathematics education. He is a recipient of the Teaching Incentive Program award at the University of South Florida. He is also the PI of a two million dollar grant from NSF, and a co_PI of a 1.4 million grant from HHMI to improve STEM education at USF.

Klappentext
Mathematical Statistics with Applications provides a calculus-based theoretical introduction to mathematical statistics while emphasizing interdisciplinary applications as well as exposure to modern statistical computational and simulation concepts that are not covered in other textbooks. Includes the Jackknife, Bootstrap methods, the EM algorithms and Markov chain Monte Carlo methods. Prior probability or statistics knowledge is not required.

Inhalt
Preface, Descriptive Statistics, Basic Concepts from Probability Theory, Additional Topics in Probability, Sampling Distributions, Point Estimation, Interval Estimation, Hypothesis Testing, Linear Regression Models, Design of Experiments, Analysis of variance, Bayesian Estimation and Inference, Nonparametric tests, Empirical Methods, Some issues in statistical applications- an overview, Appendices