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

Autori
Lovričević, Neda ; Pečarić Đilda ; Pečarić Josip

Izvornik
Journal of inequalities and applications (1029-242X) 2018 (2018), 36; 36-1

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

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 Zipf-Mandelbrot 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA