Abstract
A new empirico-statistical model is suggested to distinguish dependent narrative texts from independent narrative texts by means of their volume functions. A “regard for information” principle and an “amplitude correlation” principle are formulated. The model and both principles are examined experimentally using specific historical texts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Complete Collection of Russian Chronicles. Vol. 35. Moscow: Nauka, 1980. (In Russian.)
Complete Collection of Russian Chronicles. Vol. 33. Leningrad: Nauka, 1977. (In Russian.)
deHaan, L. and S. T. Rachev. “Estimates of the Rate of Convergence for Max-Stable Processes.”Annals of Probability, 17 (1989), 651–77.
Fedorov, E. F.Famous Italian Cities. Moscow: Moscow Univ. Press, 1985.
Fedorov, V. V. and A. T. Fomenko. “Statistical Estimation of Chronological Nearness of Historical Texts.”Journal of Soviet Mathematics, 32, 6 (1986), 668–75.
Fomenko, A. T. “Certain Statistical Regularities of Information Density Distribution in Texts with Scale.”Semiotika i Informativa. Moscow. Vol. 15 (1980), 99–124. (In Russian.)
Fomenko, A. T. “Some New Empirico-Statistical Methods of Dating and the Analysis of present Global Chronology.” (1981) (English translation is catalogued in the British Library, Department of Printed Books, Cup. 918/87).
Fomenko, A. T. “A Method for Duplicate Recognition and Some Applications.”Doklady Akademii Nauk, 258, 6 (1981), 1326–30. (In Russian.)
Fomenko, A. T. “New Empirico-Statistical Methods for Ordering Texts and Applications to Dating Problems.”Doklady Akademii Nauk, 268, 6 (1983), 1322–27. (In Russian.)
Fomenko, A. T. “New Empirical and Statistical Methods for Recognizing Parallels and Duplicate Dating.”Problemy Ustoichivosti Stokhasticheskikh Modelei. Systems Research Institute, Moscow, Workshop Proceedings, 1984, pp. 154–77. (In Russian.)
Fomenko, A. T. “Informative Functions and Related Statistical Regularities.” Statistika-Veroyatnost', Ekonomik Ser, Uchenye Zapiski po Statistike. Moscow: Nauka, 1985, pp. 335–42. (In Russian.)
Fomenko, A. T. “Duplicates in Mixed Sequences and Frequency Decay Principle.”Abstracts of Communications of the Fourth International Vilnius Conference on Probability Theory and Mathematical Statistics. Institute of Mathematics and Cybernetics of AN LSSR, 3, 1985, pp. 246-48. (In Russian.)
Galambos, J.The Asymptotic Theory of Extreme Order Statistics. New York: Wiley, 1978.
Gregorovius, F.History of the City of Rome in the Middle Ages. London: G. Bell & Sons, 1900-09.
Kalashnikov, V. V., S. T. Rachev and A. T. Fomenko. “New Methods for Comparing Volume Functions of Historical Texts.”Problemy ustoichivosti stokhasticheskikh modelei. Systems Research Institute, Moscow, Workshop Proceedings, 1986, pp. 33–45. (In Russian.)
Kalbfleisch, J. D. and R. L. Prentice.The Statistical Analysis of Failure Data. New York: John Wiley, 1980.
Kohlrausch, F. A.History of Germany, from the Earliest Period to the Present Time. New York: D. Appleton and Co., 1896.
Morozov, N. A.Christ. Volumes 1–7. Moscow-Leningrad: Gosizdat, 1924–1932. (In Russian.)
Morozova, L. E. “Application of Quantitative Methods to the Analysis of the So-called Philaret's Manuscript — The Literary Moment of the Troubled Times.”Mathematischeskie Metody i EVM v Istorischekikh Issledovaniyakh. Moscow: Nauka, 1985, pp. 182–203.
Omey, E. and S. Rachev. “On the Rate of Convergence in Extreme Value Theory.”Theoria Verojamostei i Primenenia, 3 (1988), 601–07. (To appear also inTheory Probability and its Applications.)
Rachev, S. T. “On a Class of Minimal Functionals on a Space of Probability Measures.”Theory Probability and its Applications, 29 (1984),41–49.
Rachev, S. T. “The Monge-Kantorovich Mass Transference Problem and its Statistic Applications.”Theory Probability and its Applications, 29 (1984), 647–76.
Rachev, S. T. “The Stability of Stochastic Models.”Applied Probability Newsletter, 12, 2 (1988), 3–4.
Rachev, S. T. “The Problem of Stability in Queueing Theory.”Queueing Systems Theory and Applications, 4 (1989), 287–318.
Resnick, S. I.Extreme Values, Regular Variation, and Point Processes. New York: Springer-Verlag, 1987.
Sergeev, V. S.Essays on the History of Ancient Rome. Moscow, 1938. (In Russian.)
Smith, R. L. “Uniform Rates of Convergence in Extreme-Value Theory.”Advances in Applied Probability, 14 (1982), 600–22.
The Primary Russian Chronicle. Moscow: Khud. Lit. Press, 1978. (In Russian.)
Titus Livius.Works. Cambridge, London: Heinemann, Harvard University Press, 1914.
Author information
Authors and Affiliations
Additional information
Anatoliy T. Fomenko (Dr. Sci. in mathematics, Lomonosov State University) is a Professor at Lomonosov State University, Moscow. He is author of twelve monographs and textbooks, and is co-author of the two-volume Modern Geometry (Springer-Verlag). He is also artist and historian.
Svetlozar T. Rachev (Dr. Sci., Steklov Mathematical Institute) is a Professor at the University of California, Santa Barbara. He has published more than seventy papers and is co-author of the monographMathematical Models for Construction of Queuing Models (Moscow, 1988). His main interests are: stability of stochastic models, theory of probability metrics, queuing theory and survival models.
Rights and permissions
About this article
Cite this article
Fomenko, A.T., Rachev, S.T. Volume functions of historical texts and the amplitude correlation principle. Comput Hum 24, 187–206 (1990). https://doi.org/10.1007/BF00117342
Issue Date:
DOI: https://doi.org/10.1007/BF00117342