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Random Variables and Stable Distributions on Fractal Cantor Sets

1
Young Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia 57169-63896, Iran
2
Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta 99628, Turkey
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(2), 31; https://doi.org/10.3390/fractalfract3020031
Received: 6 May 2019 / Revised: 6 June 2019 / Accepted: 9 June 2019 / Published: 11 June 2019
In this paper, we introduce the concept of fractal random variables and their related distribution functions and statistical properties. Fractal calculus is a generalisation of standard calculus which includes function with fractal support. Here we combine this emerging field of study with probability theory, defining concepts such as Shannon entropy on fractal thin Cantor-like sets. Stable distributions on fractal sets are suggested and related physical models are presented. Our work is illustrated with graphs for clarity of the results. View Full-Text
Keywords: fractal thin Cantor-like sets; fractal random variable; fractal Shannon entropy; fractal stable distributions fractal thin Cantor-like sets; fractal random variable; fractal Shannon entropy; fractal stable distributions
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Khalili Golmankhaneh, A.; Fernandez, A. Random Variables and Stable Distributions on Fractal Cantor Sets. Fractal Fract 2019, 3, 31.

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