Unbounded Growth Model for Word Frequencies in Political Transition

Abstract

Frequencies of some words appearing in a vernacular newspaper are studied. Usages of certain politically flavoured words are without any bound during poll time. Cumulative frequencies of some such words appearing in a vernacular daily from West Bengal are modeled by an unbounded growth curve $y(t) = e^{b\exp (\mathit{ct})},b> 0,c> 0;t \in (0,\infty ),$ resembling the structure of a Gompertz model. The present study is a relook at the same data set considered in Dasgupta (Growth curve and structural equation modeling, 1st edn. Springer proceedings in mathematics & statistics. Springer, New York, 2015) in a different approach. Such studies have relevance in prediction of poll results. Estimates of the model parameters are obtained from observed data over the period 2001–2010, covering several elections in India. Unbounded growth models in continuous time and discrete time are discussed in terms of interrelated proliferation rates.