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Modification of Zipf-Mandelbrot Law for Text Analysis using Linear Regression
Background: The application of Zipf’s law is ubiquitous in linguistics and other fields. Mandelbrot proposed a modification of the law called Zipf-Mandelbrot law (ZM). An enhanced form of ZM law has been proposed. Methods: In this paper, we approximate the logarithmic form of ZM law into a linear regression form of arbitrary order of the inverse of the Zipfi an rank of words in a text. The maximum likelihood solution of the regression model is given in closed form. This is in contrast to the complex search for the optimum solution of the enhanced ZM models. Findings: The performance of the proposed model is shown to compare favorably with that of ZM law as well as other existing models using Chi-Square goodness of fit test. Improvements: The present work addresses mainly the lower ranks, so we propose to extend the work to higher order ranks using LNRE model in the future.
Goodness of Fit, Linear Regression, Quantitative Linguistics, Zipf-Mandelbrot Law.
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