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## Description

Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions.

Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al.

Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research

Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al.

Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs. There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research

### Key Features

- density functions automatically determined from samples
- Free of assuming density forms
- Computation-effective methods suitable for PC

### Readership

Statisticians and academic researchers.

## Table of Contents

Preface
Chapter 1. Randomness and probability
Chapter 2. Inference and statistics
Chapter 3. Random numbers and their applications
Chapter 4. Approximation and B-spline function
Chapter 5. Disorder, entropy and entropy estimation
Chapter 6. Estimation of 1-D complicated
distributions based on large samples
Chapter 7. Estimation of 2-D complicated distributions based on large samples
Chapter 8. Estimation of 1-D complicated distribution based on small samples
Chapter 9. Estimation of 2-D complicated distribution based on small samples
Chapter 10. Estimation of the membership function
Chapter 11. Code specifications
Bibliography
Index

## Details

- No. of pages:
- 298

- Language:
- English

- Copyright:
- © 2006

- Published:
- 15th August 2006

- Imprint:
- Elsevier Science

- Print ISBN:
- 9780444527967

- Electronic ISBN:
- 9780080463858

## About the editor

### Zhi Zong

#### Affiliations and Expertise

Dalian University of Technology, Department of Naval Architecture, Dalian, China