Optimization of parameters in the Menzerath-Altmann law. (English) Zbl 1275.91115

Summary: Four formulas of the Menzerath-Altmann law are tested from the point of view of their applicability and suitability. The accuracy of related approximations of measured data is examined by the least square method at first. Then the accuracy of the calculated parameters in the formulas under consideration is compared statistically. The influence of the neglecting parameter \(c\) is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics.


91F20 Linguistics
62P25 Applications of statistics to social sciences
62J05 Linear regression; mixed models
Full Text: Link


[1] Altmann, G.: Prolegomena to Menzerath’s law. Glottometrika 2, 2, (1980), 1-10.
[2] Altmann, G., Schwibbe, M. H.: Das Menzerathsche Gesetz in informations - verarbeitenden Systemen. Olms, Hildesheim, 1989.
[3] Andres, J.: On de Saussure’s principle of linearity and visualization of language structures. Glottotheory 2, 2, (2009), 1-14.
[4] Andres, J.: On a conjecture about the fractal structure of language. Journal of Quantitative Linguistics 17, 2, (2010), 101-122.
[5] Andres, J., Benešová, M.: Fractal analysis of Poe’s Raven. Glottometrics 21 (2011), 73-98.
[6] Cramer, I.: The parameters of the Altmann-Menzerath law. Journal of Quantitative Linguistics 12, 1,(2005), 41-52. · Zbl 05431606
[7] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models. Regularity and Singularities. Academia, Prague, 2007.
[8] Hřebíček, L.: The constants of Menzerath-Altmann’s law. Glottometrika. 12 (1990), 61-71.
[9] Hřebíček, L.: Text Levels. Language Constructs, Constituents and the Menzerath-Altmann Law. Wissenschaftlicher Verlag Trier, Trier, 1995.
[10] Hřebíček, L.: Text in Semantics. The Principle of Compositeness. Oriental Institute of the Academy of Sciences of the Czech Republic, Prague, 2007.
[11] Köhler, R.: Das Menzerathsche Gesetz auf Satzebene. Glottometrika 4 (1982), 103-113.
[12] Köhler, R.: Zur Interpretation des Menzerathschen Gesetzes. Glottometrika 6 (1984), 177-183.
[13] Köhler, R., Schwibbe, M. H.: Das Menzerathsche Gesetz als Resultat des SprachverarbeitungsmechanismusDas Menzerathsche Gesetz in informations - verarbeitenden Systemen. Altmann, G. und Schwibbe, M. H. (eds.): Das Menzerathsche Gesetz in informations - verarbeitenden Systemen Olms, Hildesheim, 1989, 108-116.
[14] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Palacký University, Olomouc, 2000)
[15] Kulacka, A.: The coefficients in the formula for the Menzerath-Altmann law. Journal of Quantitative Linguistics 17, 4, (2010), 257-268.
[16] Kulacka, A., Mačutek, J.: A discrete formula for the Menzerath-Altmann law. Journal of Quantitative Linguistics 14, 1 (2007), 23-32. · Zbl 05431783
[17] Pázman, A: Foundations of Optimum Experimental Design. D. Reidel, Dordrecht, 1986. · Zbl 0588.62117
[18] Prün, C.: Validity of Menzerath-Altmann’s law: graphic representation of language, information processing systems and synergetic linguistics. Journal of Quantitative Linguistics 1, 2 (1994), 148-155. · Zbl 05431701
[19] Tučková, M: Optimal Design of Regression Experiments. Diploma Thesis, Palacký University, Olomouc, 2010
[20] Wimmer, G., Altmann, G.: Unified derivation of some linguistic laws. Köhler, R., Altmann, G., Piotrowski, R. G.: Quantitative Linquistics. An International Handbook. De Gruyter, Berlin, 2005, 791-807.
[21] Wimmer, G., Altmann, G., Hřebíček, L., Ondrejovič, S., Wimmerová, S.: Introduction to the Analysis of Texts. Veda, Bratislava, 2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.