Ebook: Mathematical Statistics
- Tags: Probability Theory and Stochastic Processes, Statistics for Business/Economics/Mathematical Finance/Insurance
- Series: Die Grundlehren der mathematischen Wissenschaften 156
- Year: 1969
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Ever since my days as a student, economists, doctors, physiologists, biologists, and engineers have come to me with queries of a statistical nature. This book is the product of my long interest in practical solutions to such problems. Study of the literature and my own ideas have repeat edly led me to improved methods, which will be established here and applied to instructive examples taken from the natural and social sciences. Thus, I hope to help the reader avoid the many fruitless direc tions in which I worked at first. The examples are not artificially con structed from theoretical considerations but are instead taken from real situations; consequently, many of the examples require detailed explana tion. The presentation of the basic mathematical concepts is, I hope, as brief as possible without becoming incomprehensible. Some rather long theoretical arguments have been necessary, but, whenever possible, references for the more difficult proofs have been made to good text books already in existence. There would be no point in developing again the mathematical theories which have been presented clearly and in detail by Kolmogorov, Caratheodory, and Cramer.
Content:
Front Matter....Pages N1-XI
Introduction....Pages 1-2
General Foundations....Pages 3-23
Probabilities and Frequencies....Pages 24-51
Mathematical Tools....Pages 52-66
Empirical Determination of Distribution Functions, Expectations, and Standard Deviations....Pages 67-88
Fourier Integrals and Limit Theorems....Pages 89-107
Gauss Theory of Errors and Student’s Test....Pages 108-126
Method of Least Squares....Pages 127-150
Estimation of Unknown Constants....Pages 151-184
Inferences Based on Observed Frequencies....Pages 185-211
Bio-Assay....Pages 212-224
Hypothesis Testing....Pages 225-266
Order Tests....Pages 267-300
Correlation....Pages 301-338
Tables....Pages 339-358
Back Matter....Pages 359-371
Content:
Front Matter....Pages N1-XI
Introduction....Pages 1-2
General Foundations....Pages 3-23
Probabilities and Frequencies....Pages 24-51
Mathematical Tools....Pages 52-66
Empirical Determination of Distribution Functions, Expectations, and Standard Deviations....Pages 67-88
Fourier Integrals and Limit Theorems....Pages 89-107
Gauss Theory of Errors and Student’s Test....Pages 108-126
Method of Least Squares....Pages 127-150
Estimation of Unknown Constants....Pages 151-184
Inferences Based on Observed Frequencies....Pages 185-211
Bio-Assay....Pages 212-224
Hypothesis Testing....Pages 225-266
Order Tests....Pages 267-300
Correlation....Pages 301-338
Tables....Pages 339-358
Back Matter....Pages 359-371
....