7 research outputs found
ZipfāMandelbrot law, f-divergences and the Jensen-type interpolating inequalities
Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate this approach with the well known ZipfāMandelbrot law applied to various types of f-divergences and distances, such are KullbackāLeibler divergence, Hellinger distance, Bhattacharyya distance (via coefficient), Ļ2-divergence, total variation distance and triangular discrimination. Addressing these applications, we firstly deduce general results of the type for the CsiszĆ”r divergence functional from which the listed divergences originate. When presenting the analyzed inequalities for the ZipfāMandelbrot law, we accentuate its special form, the Zipf law with its specific role in linguistics. We introduce this aspect through the Zipfian word distribution associated to the English and Russian languages, using the obtained bounds for the KullbackāLeibler divergence. Ā© 2018, The Author(s)
ZipfāMandelbrot law, f-divergences and the Jensen-type interpolating inequalities
Motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities, in this paper we integrate this approach with the well known ZipfāMandelbrot law applied to various types of f-divergences and distances, such are KullbackāLeibler divergence, Hellinger distance, Bhattacharyya distance (via coefficient), Ļ2-divergence, total variation distance and triangular discrimination. Addressing these applications, we firstly deduce general results of the type for the CsiszĆ”r divergence functional from which the listed divergences originate. When presenting the analyzed inequalities for the ZipfāMandelbrot law, we accentuate its special form, the Zipf law with its specific role in linguistics. We introduce this aspect through the Zipfian word distribution associated to the English and Russian languages, using the obtained bounds for the KullbackāLeibler divergence. Ā© 2018, The Author(s)