Statistics. Volume 3: Categorical and Time Dependent Data Analysis

Kunihiro Suzuki
Kaigan Minato-ku, Tokyo, Japan

Series: Mathematics Research Developments
BISAC: MAT029020




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We utilize statistics when we evaluate TV program ratings, predict voting outcomes, prepare stock, predict the amount of sales, and evaluate the effectiveness of medical treatment. We want to predict the results not on the basis of personal experience or images, but on the basis of corresponding data. The accuracy of the prediction depends on the data and related theories. It is easy to show input and output data associated with a model without understanding it. However, the models themselves are not perfect, because they contain assumptions and approximations in general. Therefore, the application of the model to the data should be careful. We should know what model we should apply to the data, what parameters are assumed in the model, and what we can state based on the results of the models.

Let us consider a coin toss, for example. When we perform a coin toss, we obtain a head or a tail. If we try the toss a coin three times, we may obtain the results of two heads and one tail. Therefore, the probability that we obtain for heads is , and the one that we obtain for tails is . This is a fact and we need not to discuss this any further. It is important to notice that the probability ( ) of getting a head is limited to this trial. Therefore, we can never say that the probability that we obtain for heads with this coin is , in which we state general characteristics of the coin. If we perform the coin toss trial 400 times and obtain heads 300 times, we may be able to state that the probability of obtaining a head is as the characteristics of the coin. What we can state based on the obtained data depends on the sample number. Statistics gives us a clear guideline under which we can state something is based on the data with corresponding error ranges.

Mathematics used in statistics is not so easy. It may be tough work to acquire the related techniques. Fortunately, software development makes it easy to obtain results. Therefore, many members who are not specialists in mathematics can perform statistical analysis with these types of software. However, it is important to understand the meaning of the model, that is, why some certain variables are introduced and what they express, and what we can state based on the results. Therefore, understanding mathematics related to the models is invoked to appreciate the results.
In this book, the authors treat models from fundamental ones to advanced ones without skipping their derivation processes. It is then possible to clearly understand the assumptions and approximations used in the models, and hence understand the limitation of the models.
The authors also cover almost all the subjects in statistics since they are all related to each other, and the mathematical treatments used in a model are frequently used in the other ones.

Additionally, many good practical and theoretical books on statistics are presented [1]-[10]. However, these books are oriented to special cases: Fundamental, mathematical, or special subjects. The author also aims to connect theories to practical subjects. He hopes that this book will aid readers in furthering their knowledge of special cases in statistics.
(Imprint: Nova)


Chapter 1. Customer Satisfaction Analysis

Chapter 2. Independent Factor Analysis

Chapter 3. Statistical Testing and Predictions

Chapter 4. Score Evaluation

Chapter 5. AHP (Analytic Hierarchy Process)

Chapter 6. Quantification Theory I

Chapter 7. Quantification Theory II

Chapter 8. Quantification Theory III (Correspondence Analysis)

Chapter 9. Quantification Theory IV

Chapter 10. Survival Time Probability

Chapter 11. Population Prediction

Chapter 12. Random Walk

Chapter 13. A Markov Process

Chapter 14. Random Number

Chapter 15. Matrix Operation

Chapter 16. AppendixA Related Mathematics

Chapter 17. Appendix B Summary of Probability Distributions and their Moments



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

Keywords: CS analysis, objective variable, explanatory variable, average, unbiased variance, co-variance, correlation factor, improve requested, Contributed item, CS correlation factor, first principal component, independent value, independent factor, adjust residual, level achievement ratio, contributed item, improvement request item, CS plot, CS correlation factor, testing, prediction, hypothesis, T distribution, F distribution, score evaluation, average, standard deviation, normalized value, extended normalized value, unit vector, AHP, pair comparison method, geometric average, eigenvector method, quantification theory I, quantification theory II, quantification theory III, correspondence analysis, quantification theory IV, Lagrange function, survival probability, Kaplan-Meier product-limit predictive method, hazard function, population prediction, cohort ratio, birth ratio, random walk, principle of symmetry, return frequency, Markov process, random walk, transition probability, transition matrix, initial vector, supply source, vanishing monitor, constant flux, initial condition, network matrix, network path with a loop, random number, exponential distribution, Poisson distribution, normal distribution, standard normal distribution, matrix operation, Gauss elimination method, LU decomposition, LU division, inverse matrix, determinant of a matrix, eigenvalue, power method, Jacobi method for symmetrical matrix, N-th product of matrix

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