Statistics. Volume 1: The Fundamentals

Kunihiro Suzuki
Fujitsu, Kaigan, Minato-ku, Tokyo, Japan

Series: Mathematics Research Developments
BISAC: MAT029000




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We utilize statistics in our daily life: when we evaluate TV program ratings, predict voting results, prepare stocks, make sales predictions, and when we evaluate the effectiveness of medical treatments. We predict the results not on the basis of personal experience, but on the basis of data. However, the accuracy of the prediction depends on the data, the theory, and the depth of understanding of the model used. This book consists of three volumes: The first volume covers the fundamentals of statistics; The second volume discusses multiple variable analyses; and the third volume covers categorical and time dependent data analysis.

In this volume, consisting of the fundamentals of statistics, we study average, variance, and probability functions. Probability functions are characterized by their moments, and we also study various techniques to evaluate these moments. In this book, we cover fundamental models to advanced models without skipping their derivation processes. We can then clearly understand the assumptions and approximations used in each model, and hence, understand the limitations of the models. We also discuss almost all of the subjects in statistics, since they are all related to each other.

Although this book includes advanced models, readers who are not statisticians can easily understand the content, since we work our way up the derivations from the fundamental level to advanced levels without skipping any. We do hope that the readers will come away with an understanding of the meaning of the models in statistics, and the techniques used to reach the final results.


Chapter 1. Sets

Chapter 2. Probability

Chapter 3. Characteristics of data in a set

Chapter 4. Probability distributions

Chapter 5. A normal distribution

Chapter 6. Probability distributions for converted variables

Chapter 7. Expectations of a probability variable

Chapter 8. Probability generating functions

Chapter 9. A cumulant expansion of a probability variable

Chapter 10. A Pearson function family

Chapter 11. A central limit theorem

Chapter 12. A sample and a population

Chapter 13. Stock


Keywords: Statistics, Permutation, Combination, Binominal, Probability, Sample space, Conditional probability, Independence

This book is available for students and members who want to be professionals in this field

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