## Table of Contents

**Table of Contents**

Acknowledgment

Preface

Reminder

Introduction

Chapter 1. Methods of Statistical Hypotheses Testing

Chapter 2. The Bayesian Problem of Hypotheses Testing

Chapter 3. Investigation of Hypotheses Acceptance Regions in Constrained Bayesian Tasks

Chapter 4. Investigations for Normal Distribution

Chapter 5. Sequential Analysis Approach

Chapter 6. Software for Statistical Hypotheses Testing

Chapter 7. Experimental Research

Concluding Remarks

Bibliography

Appendix A

Appendix B

Appendix C

**Reviews**

“Hypothesis testing is one of the basic branches of mathematical statistics which is very important for other problems of statistics and has a great application to many theoretical and practical problems. The first statement of the problem and its solution, applying t-test, was realized by Student at the beginning of the previous century.” READ MORE… – **Alexander Topchishvili, Professor, Dr. Habil. Ing.**

“The monograph suggests a new approach to the statistical hypothesis testing, the constrained Bayesian method (CBM). It maintains all the benefits of the basic methods of hypotheses testing. Namely, it uses a data-dependent measure like in Fisher’s test; for making decision it exploits a posteriori probabilities like in Jeffrey’s test and compute Type 1 and Type 2 error probabilities like in Neyman-Pearson’s approach.” READ MORE… – **Sergei Chobanyan, Visiting Professor of Department of Statistics, Michigan State University, USA**

**Keywords**: Statistical Hypotheses Testing; Constrained Bayesian Methods; The Parallel Methods; The Sequential Methods; Simple, Composite, Multiple and Directional Hypotheses Testing Methods

The book will be useful for undergraduates and postgraduates in the field of mathematics, mathematical statistics, applied statistics and application of statistical methods in research; Researchers in the areas of hypotheses testing and estimation theory who develop new methods as well as apply these methods to the solution of problems in different spheres of knowledge. The new approach gives to the young generation modern tools for novel, considerable achievements for solving theoretical and applied problems of mathematical statistics. Thus the book is very useful and necessary exactly for the students (coming generation) as it gives them new methods and opportunities for research.