Gap formation - Revision history

Ahans at 09:57, 11 July 2006

2006-07-11T09:57:23Z

2006-07-02T14:45:13Z

2006-06-27T13:36:00Z

2006-06-27T13:35:24Z

2006-02-22T12:21:44Z

2006-02-10T16:54:29Z

2006-01-15T10:31:00Z

2006-01-14T14:47:44Z

2006-01-14T14:25:43Z

2006-01-07T14:54:45Z

← Older revision		Revision as of 09:57, 11 July 2006
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−	<div align="center">[[Image:~~Tabelle11_GF~~.jpg]]</div>	+	<div align="center">[[Image:Tabelle111_GF.jpg]]</div>


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−	~~<div align="center">Table 2</div>~~	+	<div align="Center">[[Image:Tabelle2_GF.jpg ]]</div>
−	~~<div align="center">Distances between the name “Nihat” in a Turkish text (Hřebíček 2000)</div>~~
−
−	<div align="Center">[[Image:~~Tabelle_2_GF~~.jpg ]]</div>

← Older revision		Revision as of 14:45, 2 July 2006
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−	'''4. Author''': G. Altmann, L. Hřebíček	+	'''4. Author''': U. Strauss, G. Altmann, L. Hřebíček

← Older revision		Revision as of 13:36, 27 June 2006
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	<div align="center">[[Image:Tabelle11_GF.jpg]]</div>		<div align="center">[[Image:Tabelle11_GF.jpg]]</div>
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−	~~<div align="Center">[[Image:Tabelle_3_Div.jpg]]</div>~~

← Older revision		Revision as of 13:35, 27 June 2006
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−	<div align="center">~~Table 1</div>~~	+	<div align="center">[[Image:Tabelle11_GF.jpg]]</div>
−	~~<div align="center">Fitting of distance models to the data of Strauß et al~~. ~~(1984)~~</div>

	<div align="Center">[[Image:Tabelle_3_Div.jpg]]</div>		<div align="Center">[[Image:Tabelle_3_Div.jpg]]</div>

← Older revision		Revision as of 12:21, 22 February 2006
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−	'''4. ~~Authors~~''': ~~U. Strauss,~~ G. Altmann, L. Hřebíček	+	'''4. Author''': G. Altmann, L. Hřebíček

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 Solving (6) in the usual way and setting <math>e^{-t} = q</math>, one obtains the negative binomial distribution
-(7)<math>P_x = \left( \frac{k+x-1}{x}\right)p^kq^x, \quad x=0,1,2,...; \quad k>0; \quad 0<p<1; \quad q=1-p</math>
+(7)<math>P_x = \begin{pmatrix}k+x-1\\x\end{pmatrix}p^kq^x, \quad x=0,1,2,...; \quad k>0; \quad 0<p<1; \quad q=1-p</math>
 Example: Distances between equal rhythmic structures in hexameter

@@ Line 69: / Line 69: @@
-Solving (6) in the usual way and setting e-t = q, one obtains the negative binomial distribution
+Solving (6) in the usual way and setting <math>e^{-t} = q</math>, one obtains the negative binomial distribution
 (7)<math>P_x = \left( \frac{k+x-1}{x}\right)p^kq^x, \quad x=0,1,2,...; \quad k>0; \quad 0<p<1; \quad q=1-p</math>
@@ Line 79: / Line 79: @@
-<div align="center">Table 1
+<div align="center">Table 1</div>
-Fitting of distance models to the data of Strauß et al. (1984)</div>
+<div align="center">Fitting of distance models to the data of Strauß et al. (1984)</div>
 <div align="Center">[[Image:Tabelle_3_Div.jpg]]</div>
@@ Line 101: / Line 101: @@
-<div align="center">Table 2
+<div align="center">Table 2</div>
-Distances between the name “Nihat” in a Turkish text (Hřebíček 2000)</div>
+<div align="center">Distances between the name “Nihat” in a Turkish text (Hřebíček 2000)</div>
 <div align="Center">[[Image:Tabelle_2_GF.jpg ]]</div>
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 Using (2) we compute the theoretical frequency of distance 2:
-<math>NP_2=\frac{(11-2-1)!}{11!}(3(3-1)(11-3)(11-2)+3(3-1)(11-3)(11-2)+2(2-1)(11-2)(11-1)+3(3-1)(11-3)(11-2)=1.3553.</math>
+<math>NP_2=\frac{(11-2-1)!}{11!}(3(3-1)(11-3)(11-2)+3(3-1)(11-3)(11-2)+2(2-1)(11-2)(11-1)+3(3-1)(11-3)(11-2))=1.3553.</math>

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 Spang-Hanssen (1956), Yngve (1956) and Uhlířová (1967) assumed that if the probability of an entity A is p and that of non-A 1 - p = q, then the probability of a distance of size x is given simply by the geometric distribution
-(1)	<math>P_x = pq^x</math>,     x = 0,1,2,…
+(1)  <math>P_x = pq^x\quad x = 0,1,2...</math>
 which is adequate in many cases.
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 Starting from a different philosophy of texts, Hřebíček (2000) assumes that not only hierarchical relations but also sequential ones abide by the simplest form of Menzerath´s law (for derivation see Hierarchic relations) yielding
-(8)<math>y_x=ax^{-b}</math>
+(8)<math>y_x = ax^{-b}\quad </math>
 where <math>y_x</math> is the frequency of the distance x between identical units. It can be considered either as a usual function (without norming), or as a probability function representing the zeta distribution (a being the norming constant and b > 1). Testing with good results has been performed for words of high frequency in Czech and Turkish (Hřebíček 2000). Hřebíček used method (ii) for measuring distances and still another method consisting of counting the intervening sentences.

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 (3)<math>P_x= \begin{cases} P(1|1), & \quad x=0\\P(0|1)P(1|0),& \quad x=1\\P(0|1)P(0|10)P(1|00)P(0|00)^{x-2}, & \quad x=2,3,...\end{cases}</math>
-(4)<math>P_x= \begin{cases} P(1|1), & \quad x=0\\P(01|1),& \quad x=1\\P(0|1)P(00|1)P(1|100), & \quad x=2\\P(00|1)P(0|100)P(1|000)P(0|000)^{x-3}, & \quad x=3,4,...\end{cases}</math>
+(4)<math>P_x= \begin{cases} P(1|1), & \quad x=0\\P(01|1),& \quad x=1\\P(00|1)P(1|100), & \quad x=2\\P(00|1)P(0|100)P(1|000)P(0|000)^{x-3}, & \quad x=3,4,...\end{cases}</math>
 One sees that the higher the order of the chain, the more extensive is the modification of the simple geometric distribution. For example (4) can be simply written as
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 (6)<math>P^'_0(t)=-kP_0(t),</math>
 <math>P^'_x(t)=-(k+x)P_x(t)+(k-x-1)P_{x-1}(t), \quad x=1,2,3...</math>