Zipf-Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities (CROSBI ID 248617)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Lovričević, Neda ; Pečarić Đilda ; Pečarić Josip
engleski
Zipf-Mandelbrot law, f-divergences and the Jensen-type interpolating inequalities
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.
Jensen inequality ; Zipf and Zipf-Mandelbrot law ; Csiszar divergence functional ; f-divergences ; Kullback-Leibler divergence
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Podaci o izdanju
2018 (36)
2018.
36-1-36-20
objavljeno
1029-242X
1029-242X
10.1186/s13660-018-1625-y