Riemann-Liouville and Caputo Fractional Approximation of Csiszar’s $f$-Divergence
DOI:
https://doi.org/10.5644/SJM.05.1.01Keywords:
Csiszar's discrimination, Csiszar's distance, fractional calculus, Riemann-Liouville and Caputo fractional derivativesAbstract
Here are established various tight probabilistic inequalities that give nearly best estimates for the Csiszar's $f$-divergence. These involve Riemann-Liouville and Caputo fractional derivatives of the directing function $f.$ Also a lower bound is given for the Csiszar's distance. The Csiszar's discrimination is the most essential and general measure for the comparison between two probability measures. This is continuation of [4].
2000 Mathematics Subject Classification. 26A33, 26D15, 28A25, 60E15
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