Morphological productivity - Revision history

Patzschke at 12:34, 3 July 2007

2007-07-03T12:34:46Z

Patzschke at 09:19, 29 June 2007

2007-06-29T09:19:04Z

Patzschke at 09:05, 29 June 2007

2007-06-29T09:05:17Z

Patzschke at 09:04, 29 June 2007

2007-06-29T09:04:48Z

Altmann at 08:15, 29 June 2007

2007-06-29T08:15:49Z

Altmann at 14:32, 26 July 2006

2006-07-26T14:32:50Z

Ahans at 17:01, 27 June 2006

2006-06-27T17:01:58Z

Ahans at 09:09, 17 June 2006

2006-06-17T09:09:18Z

Ahans at 09:08, 17 June 2006

2006-06-17T09:08:28Z

Ahans at 10:31, 18 May 2006

2006-05-18T10:31:11Z

@@ Line 34: / Line 34: @@
 <div align="center">[[Image:Tabelle11_MP.jpg]]</div>
-(((Den Graph mit Excell machen, da 0 fehlt)
+<div align="center">[[Image:Plot2neu.png]]</div>
-Fig. 1. Fitting the Pólya distribution to the data in Table 1
+<div align="center">Fig. 1. Fitting the Pólya distribution to the data in Table 1</div>

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 (b)	Death by elimination of lexemes
-Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
+Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>\rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
 Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
 As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of  derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.

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 (1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
-<math> \frac{p}{s}, \frac{q}{s}\ge = 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>
+<math> \frac{p}{s}, \frac{q}{s}\ge  0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>
 '''Example''': Indonesian stem productivity

@@ Line 25: / Line 25: @@
 we obtain the Pólya distribution (Wimmer, Altmann 1995)
-(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, =\le p\le1, q=1-p, n \epsilon N_0</math>
+(1)<math> P_x = \frac{{-p/s \choose x}{-q/s \choose n-x}}{{-1/s \choose n}}\quad, x= 0, 1, ..., n, s>0, 0 =\le p\le1, q=1-p, n \epsilon N_0</math>
 <math> \frac{p}{s}, \frac{q}{s}\ge = 0</math> or <math> \frac{p}{s}, \frac{q}{s}\le 0</math>

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 (b)	Death by elimination of lexemes
-Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>rightarrow</math>). At the same time it is a case of specification of meaning and word prologation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
+Birth means either creation of new words or constructing them by morphological processes like derivation, reduplication, compounding etc. The construction is a case of (multidi-mensional) ''diversification'' (<math>rightarrow</math>). At the same time it is a case of specification of meaning and word prolongation. Birth and death take place in rates called birth-rate <math>\lambda_x</math>and death-rate <math>\mu_x</math> respectively.
 Since up to now only a case of derivation has been examined, the hypothesis must be restricted but we assume that it holds for other kinds of word building, too. It holds, of course, only under the condition that the given way of word buidling is actual in a language.
 As far as known, the only model was proposed by Wimmer and Altmann (1995) in which the random variable x is the number of  derivates built from a stem (x = 0,1,2,…) and <math>f_x</math> is the number of stems having x derivates.
-Another kind of productivity examined by H. Baayen will be refered in the next volume.
 '''2. Hypothesis'''
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 The creation of new morphological constructs is proportional to the class size x and can be generally symbolized as a + cx. Since creation cannot be infinite, there must be a limit n to it. The community controls the creation in the same linear way symbolized as b + (n-x-1)c. This results in the birth rate <math>\lambda = \frac{a+cx}{b+(n-x-1)c}\quad , x = 0, 1, ...n-1</math>. The death rate is similar, depending only on the class size and the morphological nature of language. It can be sym-bolized as <math>\mu = \frac{n}{n-x+1}\quad, x = 1, 2, ...,n</math>
-Inserting the above birth-rate and death-rate in the balancing birth-and-death equations (see Appendix) and reparametrizing
+Inserting the above birth-rate and death-rate in the balancing birth-and-death equations and reparametrizing
-	p = a/(a+b), q = b/(a+b), s = c/(a+b)
+p = a/(a+b), q = b/(a+b), s = c/(a+b)
 we obtain the Pólya distribution (Wimmer, Altmann 1995)

← Older revision		Revision as of 14:32, 26 July 2006
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−	'''4. Authors: G. Altmann~~'''~~	+	'''4. Authors:''' U. Strauss, G. Altmann

	'''5. References'''		'''5. References'''

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 Wimmer and Altmann (1995) studied the productivity of stems in the Indonesian dictionary (Echols, Shadily 1963). There were 6970 stems having no derivates, 1961 stems having each 1 derivate etc. The data and the results of fitting are presented in Table 1 and Fig. 1.
-<div align="center">[[Image:Tabelle1_MP.jpg]]</div>
+<div align="center">[[Image:Tabelle11_MP.jpg]]</div>
 (((Den Graph mit Excell machen, da 0 fehlt)

← Older revision		Revision as of 09:09, 17 June 2006
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	'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''		'''Wimmer, G., Altmann, G.''' (1995). A model of morphological productivity. ''J. of Quantitative Linguistics 2, 212-216.''
		+
		+	[[Category:Unfertig]]

← Older revision		Revision as of 10:31, 18 May 2006
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−	'''4. Authors: ~~U. Strauss,~~ G. Altmann'''	+	'''4. Authors: G. Altmann'''

	'''5. References'''		'''5. References'''