Morph length - Revision history

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'''1. Problem and history'''

Morph length is a specal case of length or word length (<math>\rightarrow</math>) research. The segmentation of a text in morphs is a problem depending on language and grammar (cf. Best 2001 for German).
Morph lengths are focussed in Quantitative Linguistics in different ways:
Gerlach (1982) tested the interaction of word length with morph length in a German lexicon; the hypothesis was: the more morphes a word has, the shorter the morphes are. The test results were very good. Without any data Saporta (1963: 70) proposes the hypothesis: “The mean length of morphs will be inversely related to the number of phonemes in the inventory.” This idea is said to go back to R. Jakobson (Saporta 1963: 72, footnote 15).
Here we are confronted with another hypothesis: morph lengths in texts abide by a law the same way as word lengths and other entities do.
Since up to now only a small number of data has been collected (Best 2000a, 2001a) the only distribution found rather inductively but belonging to the family of length-distributions (cf. Wimmer, Altmann 1996) was the 1-displaced Hyperpoisson distribution.
In a paper concerning morph segmentation Creutz (2003: 282) proposes the gamma distribution to be a model for morph lengths in the lexicon; but there is no proof of it. As soon as 1963 Saporta (²1966: 69) presents a little overview over morph lengths (in phonemes) in Spanish; testing the data (1679 morphs) the binomial distribution can be shown to be an acceptable model (C = 0.0166). He “cannot help wondering whether or not such a distribution is universal and, if not, what other factors correlate with different distributions.”
However, in Lakota the morphs have a specific form and their frequency distribution must be modelled by means of a difference equation of second order.

'''2. Hypothesis'''

''2.1. Morph length in texts abides by a regular probability distribution derived form the unified theory, namely the 1-displaced Hyperpoisson distribution.
2.2. If morphs have specific forms, the distribution is multimodal and must be modeled by an appropriate approach''.

'''3. Derivation'''

3.1. Substituting <math>a_0 = -1, a_1 = a, b_1 = b, a_2 = 0</math> in formula (10) of unified theory (→) and solving with displacement one obtains the Hyperpoisson distribution

(1)<math> P_x = \frac{a^{x-1}}{b^{x-1} _1 F_1 (1; b; a)}, \quad x = 1, 2, 3, ...; a, b > 0</math>

'''Example''': Morph length distribution in German

Best (2001a) used a text from Eichsfelder Tageblatt (6.3.1997, p.8): „Sieben Deutsche in Jemen entführt)“ and counting the length of morphemes he obtained the results in Table 1.

<div align="center">[[Image:Tabelle1_ML.jpg]]</div>

<div align="center">[[Image:Grafik1_ML.jpg]]</div>
<div align="center">Fig. 1. Fitting the 1-displaced Hyperpoisson distribution to morph length data</div>

3.2. In Lakota morphemes usually consist of even number of syllables. In that case the usual approach must be extended and the distribution must be modeled by a difference equation of second order i.e.

(2)<math> P_x = g(x)P_{x-1}+h(x)P_{x-2}\quad</math>.

Pustet and Altmann (2005) set g(x) = a(k + x – 1)/x and h(x) = b(2k + x – 2)/x and obtained as solution the Gegenbauer distribution given as

(3)<math> P_x = (n)=\begin{cases} (1-a-b)^k,\quad x=0 \\ p_0 \sum_{j=0}^{[x/2]}\frac{b^j k^{(x-j)}a^{x-2j}}{j!(x-2j)!}, \quad x = 1, 2, 3,...\end{cases} </math>

where [.] is the integer part and k(x - j) is the ascending factorial function.

'''Example'''. Morpheme length in Lakota

Pustet and Altmann (2005) modeled the morpheme distribution in Lakota and obtained the results in Table 2 and Fig. 2.

<div align="center">[[Image:Tabelle2_ML.jpg]]</div>

<div align="center">[[Image:Grafik2_ML.jpg]]</div>
<div align="center">Fig. 2. Fitting the Gegenbauer distribution to the Lakota data</div>

'''4. Authors: U. Strauss, G. Altmann, K.-H. Best'''

'''5. References'''

'''Best, K.-H.''' (2000a). Morphlängen in Fabeln von Pestalozzi. ''Göttinger Beiträge zur Sprachwissenschaft 3, 19-30.''

'''Best, K.-H'''. (2001a). Zur Länge von Morphen in deutschen Texten. In: Best, K.-H. (ed.), ''Häufigkeitsverteilungen in Texten: 1-14''. Göttingen: Peust & Gutschmidt.

'''Best, K.-H'''. (2005). Morphlänge. In: Köhler, R., Altmann, G., Piotrowski, R. (eds.), ''Quantitative Linguistik - Quantitative Linguistics. Ein internationales Handbuch: 255-260''. Berlin/ N.Y.: de Gruyter

'''Creutz, M'''. (2003). Unsupervised segmentation of words using prior distributions of morph length and frequency. ''Proceedings of ACL-03, The 41st Annual Meeting of th Association of Computational Linguistics: 280-287''. Sapporo, Japan, 7-12 July.

'''Gerlach, R.''' (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.

Gorot´, E.I. (1990). Izomorfnye i otličitel´nye čerty morfemy i sloga v raspredelenii dliny. In: Kvantitativnaja ''lingvistika i avtomatičeskij analiz tekstov: 32-36''. Tartu.

'''Krott, A'''. (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.

'''Nikonov, V.A'''. (1978). Dlina slova. ''Voprosy jazykoznanija 6, 104-111''.

'''Pustet, R., Altmann, G'''. (2005). Morpheme length distribution in Lakota. ''J. of Quantitative Linguistics 12(1), 53-63''.

Saporta, S. (1963, ²1966). Phoneme distribution and language universals. In: Greenberg, J.H. (ed.), ''Universals of language. Second edition. Report of a conference held at Dobbs Ferry, New York, April 13-115, 1961: 61-72''. Cambridge, Mass. & London: The M.I.T. Press.

'''Wimmer, G., Altmann, G'''. (1996). The theory of word length: some results and generalizations. ''Glottometrika 15, 112-133''.

Altmann, Gabriel (1988), Wiederholungen in Tex-
ten. Bochum: Brockmeyer.
Altmann, Gabriel/ Schwibbe, Michael H. (1989),
Das Menzerathsche Gesetz in informationsverar-
beitenden Systemen. Hildesheim: Olms.
Altmann-Fitter (1994), Lüdenscheid: RAM-Verlag.
Altmann-Fitter. Iterative Fitting of Probability
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Best, Karl-Heinz (1999), Quantitative Linguistik:
Entwicklung, Stand und Perspektive. In: Göttinger
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wissenschaft 3,19K30.
Best, Karl-Heinz (2001a), Probability Distributi-
ons of Language Entities. In: Journal of Quantita-
tive Linguistics 8,1K11.
Best, Karl-Heinz (2001b), Kommentierte Biblio-
graphie zum Göttinger Projekt. In: Best 2001,
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phen in deutschen Texten. In: Best 2001, 1K14.
Best, Karl-Heinz (2001d), Silbenlängen in Mel-dungen
der Tagespresse. In: Best 2001, 15K32.
Best, Karl-Heinz (2001e), Zur Verteilung rhyth-mischer
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in Texten. Göttingen: Peust & Gut-schmidt.
Best, Karl-Heinz/Altmann, Gabriel (1996), Pro-ject
Report. In: Journal of Quantitative Linguistics
3, 85K88.
Bunge, Mario (1977), Treatise on Basic Philoso-phy,
Vol. 3: Ontology I: The Furniture of the
World. Dordrecht: Reidel.
Fucks, Wilhelm (1956), Die mathematischen Ge-setze
der Bildung von Sprachelementen aus ihren
Bestandteilen. In: Nachrichtentechnische Fachbe-richte
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Strauss, Udo). Bochum: Brockmeyer, 95K102.
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è erty morfemy i sloga v raspredelenii dliny. In:
Kvantitativnaja lingvistika i avtomati eskij analiz
tekstov (UZTU 912), 32K36.
Greenberg, Joseph H. (1960), A Quantitative Ap-proach
to the Morphological Typology of Lan-guage.
In: International Journal of American Lin-guistics
26, 178K194.
Grotjahn, Rüdiger/Altmann, Gabriel (1993), Mo-delling
the Distribution of Word Length: Some
Methodological Problems. In: Contributions to
Quantitative Linguistics. (Eds. Reinhard Köhler/
Burghard B. Rieger). Dordrecht: Kluwer, 141K153.
H ebí ek, Lud¼ñêôœ`k (1997), Lectures on Text Theory.
Prague: Academy of Sciences of the Czech Re-public,
Oriental Institute.
Kempgen, Sebastian (1995a), Kodierung natürli-cher
Sprache auf morphologischer Ebene. In:
WSLAV XL,52K57.
Kempgen, Sebastian (1995b), Russische Sprachsta-tistik.
München: Sagner.
Köhler, Reinhard (1986), Zur linguistischen Syner-getik:
Struktur und Dynamik der Lexik. Bochum:
Brockmeyer.
Krott, Andrea (1994), Ein funktionalanalytisches
Modell der Wortbildung. Magisterarbeit, Trier.
Krott, Andrea (1996), Some Remarks on the Re-lation
between Word Length and Morpheme
Length. In: Journal of Quantitative Linguistics 3,
29K37.
Niehaus, Brigitta (1997), Untersuchung zur Satz-längenhäufigkeit
im Deutschen. In: Best, Karl-Heinz
(Hrsg.), Glottometrika 16. Trier: Wissen-schaftlicher
Verlag Trier, 213K275.
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London: Griffin.
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der deutschen Sprache. München: Deutscher Ta-schenbuch
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Karl-Heinz

@@ Line 12: / Line 12: @@
 ''2.1. Morph length in texts abides by a regular probability distribution derived form the unified theory, namely the 1-displaced Hyperpoisson distribution.''
 ''2.2. If morphs have specific forms, the distribution is multimodal and must be modeled by an appropriate approach''.
@@ Line 40: / Line 41: @@
 (3)<math> P_x = (n)=\begin{cases} (1-a-b)^k,\quad x=0  \\ p_0 \sum_{j=0}^{[x/2]}\frac{b^j k^{(x-j)}a^{x-2j}}{j!(x-2j)!}, \quad x = 1, 2, 3,...\end{cases}	 </math>
-where [.] is the integer part and k(x - j) is the ascending factorial function.
+where [.] is the integer part and k<sup>(x - j)</sup> is the ascending factorial function.
 '''Example'''. Morpheme length in Lakota

@@ Line 51: / Line 51: @@
-'''4. Authors: G. Altmann, K.-H. Best'''
+'''4. Authors: U. Strauss, G. Altmann, K.-H. Best'''
 '''5. References'''
@@ Line 58: / Line 58: @@
 '''Best, K.-H'''. (2001a). Zur Länge von Morphen in deutschen Texten. In: Best, K.-H. (ed.), ''Häufigkeitsverteilungen in Texten: 1-14''. Göttingen: Peust & Gutschmidt.
 '''Best, K.-H'''. (2005). Morphlänge. In: Köhler,  R., Altmann, G., Piotrowski, R. (eds.), ''Quantitative Linguistik - Quantitative Linguistics. Ein internationales Handbuch: 255-260''. Berlin/ N.Y.: de Gruyter
@@ Line 65: / Line 67: @@
 '''Gerlach, R.''' (1982). Zur Überprüfung des Menzerathschen Gesetzes im Bereich der Morphologie. ''Glottometrika 4, 95-102''.
-'''Gorot´, E.I.''' (1990). Izomorfnye i otličitel´nye čerty morfemy i sloga v raspredelenii dliny. In: Kvantitativnaja ''lingvistika i avtomatičeskij analiz tekstov: 32-36''. Tartu.
+'''Gorot´, E.I.''' (1990). Izomorfnye i otličitel´nye čerty morfemy i sloga v raspredelenii dliny. In: ''Kvantitativnaja lingvistika i avtomatičeskij analiz tekstov: 32-36''. Tartu.
 '''Krott, A'''. (1996). Some remarks on the relation between word length and morpheme length. ''J. of Quantitative Linguistics 3, 29-37''.
@@ Line 77: / Line 79: @@
 '''Wimmer, G., Altmann, G'''. (1996). The theory of word length: some results and generalizations. ''Glottometrika 15, 112-133''.
 [[Category:Unfertig]]

← Older revision		Revision as of 09:07, 17 June 2006
Line 173:		Line 173:
	Linguistics 1,98K106.		Linguistics 1,98K106.
	Karl-Heinz		Karl-Heinz
		+
		+	[[Category:Unfertig]]

@@ Line 35: / Line 35: @@
 .2. In Lakota, morphemes usually consist of even number of syllables. In that case the usual approach must be extended and the distribution must be modeled by a difference equation of second order i.e.
-(2)<math> P_x = g(x)P_{x-1}+h(x)P_{x-2}\quad</math>.
+(2)<math>  P_x = g(x)P_{x-1}+h(x)P_{x-2}\quad</math>.
 Pustet and Altmann (2005) set g(x) = a(k + x – 1)/x and h(x) = b(2k + x – 2)/x and obtained as solution the Gegenbauer distribution given as

@@ Line 3: / Line 3: @@
 Morph length is a specal case of length or word length (<math>\rightarrow</math>) research. The segmentation of a text in morphs is a problem depending on language and grammar (cf. Best 2001 for German).
 Morph lengths are focussed in Quantitative Linguistics in different ways:
-Gerlach (1982) tested the interaction of word length with morph length in a German lexicon; the hypothesis was: the more morphes a word has, the shorter the morphes are. The test results were very good. Without any data Saporta (1963: 70) proposes the hypothesis: “The mean length of morphs will be inversely related to the number of phonemes in the inventory.” This idea is said to go back to R. Jakobson (Saporta 1963: 72, footnote 15).
+Gerlach (1982) tested the interaction of word length with morph length in a German lexicon; the hypothesis was: the more morphs a word has, the shorter the morphs are. The test results were very good. Without any data Saporta (1963: 70) proposes the hypothesis: “The mean length of morphs will be inversely related to the number of phonemes in the inventory.” This idea is said to go back to R. Jakobson (Saporta 1963: 72, footnote 15).
-Here we are confronted with another hypothesis: morph lengths in texts abide by a law the same way as word lengths and other entities do.
+Here we are confronted with another hypothesis: morph lengths in texts abide by a law in the same way as word lengths and other entities do.
 Since up to now only a small number of data has been collected (Best 2000a, 2001a) the only distribution found rather inductively but belonging to the family of length-distributions (cf. Wimmer, Altmann 1996) was the 1-displaced Hyperpoisson distribution.
 In a paper concerning morph segmentation Creutz (2003: 282) proposes the gamma distribution to be a model for morph lengths in the lexicon; but there is no proof of it. As soon as 1963 Saporta (²1966: 69) presents a little overview over morph lengths (in phonemes) in Spanish; testing the data (1679 morphs) the binomial distribution can be shown to be an acceptable model (C = 0.0166). He “cannot help wondering whether or not such a distribution is universal and, if not, what other factors correlate with different distributions.”
@@ Line 11: / Line 11: @@
 '''2. Hypothesis'''
-''2.1. Morph length in texts abides by a regular probability distribution derived form the unified theory, namely the 1-displaced Hyperpoisson distribution.
+''2.1. Morph length in texts abides by a regular probability distribution derived form the unified theory, namely the 1-displaced Hyperpoisson distribution.''
-.2. If morphs have specific forms, the distribution is multimodal and must be modeled by an appropriate approach''.
+''2.2. If morphs have specific forms, the distribution is multimodal and must be modeled by an appropriate approach''.
 '''3. Derivation'''
@@ Line 32: / Line 32: @@
-.2. In Lakota morphemes usually consist of even number of syllables. In that case the usual approach must be extended and the distribution must be modeled by a difference equation of second order i.e.
+.2. In Lakota, morphemes usually consist of even number of syllables. In that case the usual approach must be extended and the distribution must be modeled by a difference equation of second order i.e.
 (2)<math> P_x = g(x)P_{x-1}+h(x)P_{x-2}\quad</math>.
@@ Line 44: / Line 44: @@
 '''Example'''. Morpheme length in Lakota
-Pustet and Altmann (2005) modeled the morpheme distribution in Lakota and obtained the results in Table 2 and Fig. 2.
+Pustet and Altmann (2005) modeled the morpheme length distribution in Lakota and obtained the results in Table 2 and Fig. 2.
 <div align="center">[[Image:Tabelle222_ML.jpg]]</div>

@@ Line 24: / Line 24: @@
 Best (2001a) used a text from Eichsfelder Tageblatt (6.3.1997, p.8): „Sieben Deutsche in Jemen entführt)“ and counting the length of morphemes he obtained the results in Table 1.
-<div align="center">[[Image:Tabelle1_ML.jpg]]</div>
+<div align="center">[[Image:Tabelle111_ML.jpg]]</div>
 <div align="center">[[Image:Grafik1_ML.jpg]]</div>
@@ Line 45: / Line 46: @@
 Pustet and Altmann (2005) modeled the morpheme distribution in Lakota and obtained the results in Table 2 and Fig. 2.
-<div align="center">[[Image:Tabelle2_ML.jpg]]</div>
+<div align="center">[[Image:Tabelle222_ML.jpg]]</div>
 <div align="center">[[Image:Grafik2_ML.jpg]]</div>