Characterizing Ranked Chinese Syllable-to-Character Mapping Spectrum: A Bridge Between the Spoken and Written Chinese Language

One important aspect of the relationship between spoken and written Chinese is the ranked syllable-to-character mapping spectrum, which is the ranked list of syllables by the number of characters that map to the syllable. Previously, this spectrum is analyzed for more than 400 syllables without distinguishing the four intonations. In the current study, the spectrum with 1280 toned syllables is analyzed by logarithmic function, Beta rank function, and piecewise logarithmic function. Out of the three fitting functions, the two-piece logarithmic function fits the data the best, both by the smallest sum of squared errors (SSE) and by the lowest Akaike information criterion (AIC) value. The Beta rank function is the close second. By sampling from a Poisson distribution whose parameter value is chosen from the observed data, we empirically estimate the $p$-value for testing the two-piece-logarithmic-function being better than the Beta rank function hypothesis, to be 0.16. For practical purposes, the piecewise logarithmic function and the Beta rank function can be considered a tie.

Fitting Ranked English and Spanish Letter Frequency Distribution in U.S. and Mexican Presidential Speeches

The limited range in its abscissa of ranked letter frequency distributions causes multiple functions to fit the observed distribution reasonably well. In order to critically compare various functions, we apply the statistical model selections on ten functions, using the texts of U.S. and Mexican presidential speeches in the last 1-2 centuries. Dispite minor switching of ranking order of certain letters during the temporal evolution for both datasets, the letter usage is generally stable. The best fitting function, judged by either least-square-error or by AIC/BIC model selection, is the Cocho/Beta function. We also use a novel method to discover clusters of letters by their observed-over-expected frequency ratios.