From Laws in Quantitative Linguistics
1. Problem and history
If syllables are coded in the canonical form, V, CV, CVC, etc. where the vowel (V) is the syllable nucleus and the consonant (C) is the periphery, we obtain a set of structural types whose number follows a specific two-dimensional distribution. The types can be presented in tabular form
Where the frequency of the type CVVCC is given as n12, i symbolizing the number of consonants before and j that behind the nucleus. There are at most r onsets and s codas in the syllable. Let Pij * be the corresponding probability.
The distribution of canonical syllable types abides by the (modified) bivariate Conway-Maxwell-Poisson distribution.
Starting from the unified theory we assume that the probabilities of syllable types are joined with the following proportionality relation
i.e. a class is proportional to its left or upper neighbour. In the first step Zörnig and Altmann (1993) used the simple Menzerathian relatioship (see Hierarchic relations) as proprotionality function and obtained
The solution of (2) yields
where the norming constant is .
Since the particular case examined (Indonesian) has a strong preference for the CVC type ( = n11) the distribution must be modified and renormed. Weighting P11 * by β the other probabilities must be weighted so that βP11 * + α(1 - P11 * ) = 1. As a result we obtain
Zörnig and Altmann (1993) show also the estimators won from frequency classes as
Example. Structure of Indonesian syllables
In about 15000 Indonesian word forms from different texts Zörnig and Altmann (1993) found 610 syllable types shown in Table 1.
Using (3), (4) and (5) they obtained
The estimated parameters are: a = b = 6, k = 4.585, m = 4.948, α = 0.713, β = 1.291, P * 00 = 0.014, N = 610 and the fitting is presented in Table 2. For example NP12 is computed as
The result is acceptable without testing.
4. Authors: U. Strauss, G. Altmann
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Vennemann, T. (1982) (ed.). Zur Silbenstruktur der deutschen Standardsprache. Silben, Segmente, Akzente: 261-305. Tübingen: Narr.
Zörnig, P., Altmann, G. (1993). A model for the distribution of syllable types. Glottometrika 14, 190-196.