Naslov
Zipf-Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities

Autori
Lovričević, Neda ; Pečarić, Đilda ; Pečarić, Josip

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Conference Proceedings / - , 2018, 517-517

Skup
ICAMCS 2018: 20th International Conference on Applied Mathematics and Computer Sciences

Mjesto i datum
Amsterdam, Nizozemska, 10.05.2018. - 11.05.2018

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Csiszar divergence functional, f-divergences, Jensen inequality, Kullback-Leibler divergence, Zipf and Zipf-Mandelbrot law.

Sažetak
The paper is motivated by the method of interpolating inequalities that makes use of the improved Jensen-type inequalities. This approach is integrated with the well known Zipf-Mandelbrot law applied to various types of f-divergences, such are Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance (via coefficient), chi-square divergence, total variation distance and triangular discrimination. General results are firstly deduced for the Csiszar divergence functional from which the listed divergences originate. The analyzed inequalities are presented for the ZipfMandelbrot law and then accentuated for its special form – the Zipf law with its special role in linguistics. This aspect is introduced through the Zipfian word distribution associated to the English and Russian languages, using the obtained bounds for the Kullback-Leibler divergence. Thus its experimental character is accentuated. Since this paper includes three important and widely investigated issues: the Jensen inequality, the divergences for probability distributions and the Zipf-Mandelbrot law, it can be of interest for mathematicians who investigate any of these fields with an accent put on mathematical inequalities, as well as for interdisciplinary fields (e.g. linguistics was involved in this case.)

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA