Abstract
The entropy is a measurement of disorder or a measurement of heterogeneous information and it is known that amount of information cannot be negative. There are many methods about entropies by applied derivative to a probability distribution functions. In this paper, we applied fractional order derivative to probability distribution function, and this fractional order derivative is different than many of fractional order derivative methods in literature. Tsallis entropy was obtained by applying fractional order derivative methods in literature. In this paper, a new method for fractional order derivative was applied to probability distribution functions and two new definitions for entropy computation were obtained. One of them concludes in negative values for some cases, it is known that entropy cannot be negative, so, we selected the other definition (Definition 2) for entropy computation. The obtained new definition for entropy was applied to four probability distribution functions and obtained results were compared with Shannon entropies. The experimental results illustrated that the proposed method is superior to Shannon entropy method and the better entropy values were obtained for orders in interval (0,1).
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