Information-Theoretic Methods for Estimating of Complicated Probability Distributions

Mixing up various disciplines often produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology is a useful method for estimating complicated probability distributions.

Estimating probabilistic risk analysis (PSA), machine learning, pattern recognition, image processing, neural networks and quality control. Simple distribution forms as as Gaussian, exponential or Weibull distributions, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of 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, we can expect the stock market is correct? Another case well exemplifying the necessity of reliability engineering. Failure of exact estimation of the probability of distributions under consideration may lead to disastrous designs.
It has been determined that it has been created in a very different way. The present book is intended to fill the gap.

Determining a complicated distribution is a simple task. Two important mathematical tools, function approximation and information theory, that are all traditional mathematical statistics, are often used. Several methods constructed. It is detailed in this book. These methods have been applied by many people. They are superior in the following senses:

(1) No prior information of the distribution form to be determined. It can be determined automatically from the sample;
(2) The sample size may be large or small;
(3) They are particularly suitable for computers.

It is the rapid development of computing technology.

The methods of analysis, statistics, and the presentation can be overcome by information theory.

Key Features:


- Density functions automatically determined from samples

- Free of assuming density forms

- Computation-effective methods suitable for PC

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

Preface
Chapter 1. Randomness and probability
Chapter 2. Inference and statistics
Chapter 3. Random numbers and her 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