Abstract
In the community of geodesy it is well-known that the famous normal distribution is originated from the mathematical analysis of observational errors in astronomical and geodetic measurements.
However, as far as we know this aspect of scientific history which is of considerable interest for the community of earth sciences has rarely been considered in the literature of earth sciences.
In geodesy and related areas the bivariate normal distribution is one of the most frequently used probability distributions. Nowadays, in a wide range of problems arising from diverse areas of geodesy, geophysics, photogrammetry and astronomical geodesy we encounter numerous applications of the univariate and multivariate normal distributions.
In the present paper the historical role of earth sciences in the origins of the bivariate normal distribution is briefly discussed. Some new evidences of Bravais’ contribution to the origin of the correlated bivariate normal distribution are considered. The new evidences and refinements established in this paper convey such a general methodological and intellectual content that is useful for the community of geodesy, geophysics, and furthermore in earth sciences.
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References
Adrain R 1808: In: The Analyst or Mathematical Museum. W P Farrand and Co., Philadelphia, 1, 93–109.
Agterberg F P 1974: Geomathematics: Mathematical Background and Geoscience Applications, Elsevier Scientific Publishing, Amsterdam
Anderson T W 1958: An Introduction to Multivariate Statistical Analysis. John & Wiley, New York
Anderson D N, Taylor S R 2002: Bull. Seism. Soc. Am., 92, 2391–2399.
Beaumont M 1866: In: Mémoires de l’Académie des Sciences de l’Institut Impérial de France, 35, 23–49.
Bravais A 1846: In: Mémoires presentés à l’Académie Royale des Sciences, Paris, 9, 255–332 (English translation, 1958, White Sands Proving Ground, New Mexico).
Bravais A 1850: J. Ecole Polytech., 19, 1–128.
Burkhardt F, Browne J, Porter D M, Richmond M eds 1994: The correspondence of Charles Darwin. Volume 9, 1861, Cambridge University Press
Carosio A 1989: Parameterschätzung I. Institut für Geodäsie und Photogrammetrie, ETH Zürich
Cetin H, Warner T A, Levandowsi D W 1993: Photogrammetric Engineering, Remote Sensing, 59, 1755–1764.
Detrekői Á 1991: Adjustment Calculations (in Hungarian). Tankönyvkiadó, Budapest
Dodson C T J, Oba Y, Sampson W W 2001: J. Statistical Physics, 102, 345–353.
Eisenhart C 1968: In: Intern. Enc. of the Soc. Sciences. D L Sills ed., 74–81.
Foody G M, Campbell N A, Trodd N M, Wood T F 1992: Photogrammetric Engineering, Remote Sensing, 58, 1335–1341.
Galton F 1888: In: Proceedings of the Royal Society of London, 45, 134–145.
Gauss C F 1823: Theoria Combinationis Observationum Erroribus minimis Obnoxiae, Pars Prior, Pars Posterior, Supplementum, Gottingen, or its English translation 1995
Gauss K F 1995: Theory of the Combination of Observations least Subject to Errors. Part One, Part Two, Supplement, Translated by G W Stewart, Philadelphia
Grattan-Guinness I 1970: Operational Research Quartely, 21, 361–364.
Helmert F R 1868: Zeitschrift für Mathematik und Physik, 13, No. 2, 73–120.
Kittel C 2005: Introduction to Solid State Physics. 8th Ed., University of California, Berkeley
Laplace P S 1810: In: Mémoires de l’Institut Impérial de France, 279–347.
Mois A I, Müller U, Wondratschek H 2006: Historical Introduction: International Tables for Crystallography. Springer
Monhor D 2009: 23th International Congress of History of Science and Technology. Budapest, Hungary (unpublished presentation)
Monhor D, Takemoto S 2005: J. Geod. Soc. Japan, 51, 175–185.
Pearson K 1896: Philosophical Transactions of the Royal Society of London, Series A, 187, 253–318.
Pearson K 1901: Philosophical Transactions of the Royal Society of London, Series A, 195, 1–47.
Pearson K 1920: Biometrika, 13, 25–45.
Pearson E S 1967: Biometrika, 54, 341–455.
Plana G A A 1813: In: Mémoire de L’Académie de Impériale de Turin, 20, 355–408.
Stigler S M 1986: The History of Statistics: The Measurement of Uncertainty before 1900. Harvard University Press, London
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Monhor, D. A very short note on the origins of correlated bivariate normal distribution with particular relevance to earth sciences. Acta Geod. Geoph. Hung 47, 117–122 (2012). https://doi.org/10.1556/AGeod.47.2012.1.10
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DOI: https://doi.org/10.1556/AGeod.47.2012.1.10