Steiner, Ferenc, ed. (1991) The most frequent value : introduction to a modern conception of statistics. Akadémiai Kiadó, Budapest. ISBN 963-05-5687-1
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Abstract
Contents Preface Introduction I. Most frequent value and cohesion of probability distributions (F. Steiner) II. Some mathematical comments on the most frequent value and cohesion of probability distributions (L. Csernyak) III. Adjustment of telluric straight lines (Mrs. Dona Landy — M. Lantos) IV. M-fitting in comparison with the method of least squares (F. Steiner) V. M-fitting in the processing of magnetotelluric data (L. Ferenczy) 1. Introduction 2. Basic formulae 2.1. The impedance tensor 2.2. The most frequent value 3. Program for the determination of the impedance by the method of M-fitting 4. Computational results and some conclusions 4.1. Changes in the impedance in case of far-off points 4.2. Change of the coherencies in case of far-off points 4.3. Determination of the number of data defining the impedances and estimation of the number of far-off points 5. Conclusions VI. Investigations concerning the practical computation of the most frequent value of data systems (L. Csernyak — F. Steiner) VII. Some computational aspects of the most frequent value and M-fitting problems (B. Hajagos) VIII. The median of the frequency curves of the telluric field vectors and its stability (Mrs. Ilona Landy - M. Lantos) IX. The dependence of the estimated values on the sample size n (L. Csernyak — B. Hajagos — Mrs. Ilona Landy — M. Lantos — F. Steiner) X. The most frequent value as estimation with minimum information loss (B. Hajagos) 1. Basic concepts and relations 2. Theorems 3. Proof of the theorems XI. General validity of the law of large numbers in case of adjustments according to the most frequent value (L. Csernyak — B. Hajagos — F. Steiner) XII. Monte Carlo studies on the rate of fulfillment of the law of large numbers (L. Csernyak — F. Steiner) XIII. Correlation according to the most frequent value (F. Steiner) 1. The correlation coefficient according to the most frequent value 2. Regression line according to the most frequent value 3. Some geophysical-geological examples for the use of the correlation and regression analysis according to the most frequent value 3.1. The connection of AL2O3 — k.SiO2 with the natural gamma indication 3.2. Connection between the Zr-content and the riebeckite + egirine content 3.3. Connection between the boehmite content and the natural gamma indication XIV. Weighted M-fitting (F. Steiner) XV. Investigations concerning the existence and de termination of the most frequent value and epsilon (L. Csernyak) APPENDICES App. I. A practical example for the Cauchy distribution (Mrs. Ilona Landy — M. Lantos) App. II. Approximation by orthogonal functions according to the most frequent value (F. Steiner) App. III. A practical study on the validity of the law of large numbers (Mrs. Ilona Landy) App. IV. On the inadequacies of the concept of scatter (F. Steiner) App. V. An elementary justification of the special form of weight function in the computation of the most frequent value (B. Hajagos) App. VI. The most frequent value as a robust estimate (L. Csernyak) App. VII. A remark on optimality of the most frequent value as a robust estimate (L. Csernyak) App. VIII. Introductory instructions for the computation of the most frequent value of a series of data (F. Steiner) App. IX. The inadequacy of the Heisenberg relation in generally posed questions of uncertainties (L. Csernyak — F. Steiner) 1. Introduction 2. A trivial property of the mostly used transform pairs which is often but falsely enhanced as the very content of the Heisenberg relation 3. Definitions for the ‘'length” or ‘‘width” of functions 4. Examples for the decision between function pairs belonging to a given integral transform 5. Examples for Fourier-pairs of functions and distributions, respectively 6. The measure of the uncertainty used by Heisenberg 7. Remarks, questions, meditations 8. Conclusions Summary Concise presentation of most frequent value procedures in a general statistical framework (F. Steiner) Bibliography of articles written in the theme of most frequent value procedures and in closely related topics Name and subject index
| Item Type: | Book |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QE Geology / földtudományok |
| Depositing User: | András Horuczi |
| Date Deposited: | 27 Mar 2025 11:56 |
| Last Modified: | 27 Mar 2025 11:56 |
| URI: | https://real-eod.mtak.hu/id/eprint/19907 |
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