View More View Less
  • 1 Miskolci Egyetem Geofizikai Tanszék Egyetemváros HU–3515 Miskolc
  • | 2 University of Miskolc Institute of Mathematics 3515 Miskolc, Egyetemváros
Restricted access

On the basis upon n corresponding value-pairs (xi; yi), i = 1, …, n, the closeness of correspondence between the random variables x and h is customarily characterized by the classical correlation coefficient r (see Eq. (2) in the present paper), equally in the geosciences and in the everyday life. It is shown in the present paper the lack of the robustness of Eq. (2) (r has even no meaning for circa 40% of the types occurring in the geosciences), and the lack of the resistance (one single outlying value-pair can distort the r-value in an incredible degree). The modern correlation coeffcient rrob (see Eq. (9) in this paper) is completely resistant against outliers, and in the same time also robust: Eq. (9) is applicable even if x and h are of Cauchy type, very far lying from the Gaussian distribution and even from the most frequently occurring so-called statistical distribution (see Eq. 6). For the Cauchy distribution neither the scatter (variance) nor the expected value exist therefore for this distribution-type even the classical theoretical value (see Eq. 3) does not exist: the calculation of r according to Eq. (2) gives in this case an "estimation" of a not existing quantity. In the paper are presented the results of a time consuming series of Monte Carlo calculations made equally for the statistical and Gaussian distributions and for n = 10;   30 and   100; the errors characterized by the semi-interquartile and semi- intersextile ranges of the modern rrob (Eq. 9) were calculated and tabulated for rt = 0; 0.1; 0. 2; … 0. 7 and 0. 8. An approximate method is also given (see the simple Eqs 16 and 17) to determine that value of n which assures a prescribed accuracy of the modern rrob.

  • Steiner F, Hajagos B 2001: Magyar Geofizika, 42, 2.

    () 42 Magyar Geofizika .

  • Cramér H 1945: Mathemetical Methods of Statistics. Almqvist and Wiksells, Uppsala

    Mathemetical Methods of Statistics , ().

  • Dutter R 1986/1987: Mathematische Methoden in der Montangeologie. Vorlesungsnotizen, Manuscript, Leoben

  • Huber P J 1981: Robust Statistics, Wiley, New York

  • Steiner F 1990: Introduction to Geostatistics (in Hungarian). Tankönyvkiadó, Budapest

    Introduction to Geostatistics (in Hungarian) , ().

  • Steiner F ed. 1997: Optimum Methods in Statistics. Akadémiai Kiadó, Budapest

    Optimum Methods in Statistics , ().

  • Anscombe F J 1960: Technometrics, 2, 123--147.

    () 2 Technometrics : 123 -147.

AGG Editorial Office
Address: P.O. Box 5, H-9401 Sopron, Hungary
Phone: (36 99) 508 340
Fax: (36 99) 508 355
E-mail: actagg@ggki.hu

  • Impact Factor (2019): 0.909
  • Scimago Journal Rank (2019): 0.337
  • SJR Hirsch-Index (2019): 18
  • SJR Quartile Score (2019): Q3 Building and Construction
  • SJR Quartile Score (2019): Q3 Geology
  • SJR Quartile Score (2019): Q3 Geophysics
  • Impact Factor (2018): 0.942
  • Scimago Journal Rank (2018): 0.314
  • SJR Hirsch-Index (2018): 17
  • SJR Quartile Score (2018): Q3 Geology
  • SJR Quartile Score (2018): Q3 Geophysics

For subscription options, please visit the website of Springer Nature.

Acta Geodaetica et Geophysica
Language English
Size B5
Year of
Foundation
2013
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó Springer
Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 2213-5812 (Print)
ISSN 2213-5820 (Online)