Random Variables and Stable Distributions on Fractal Cantor Sets
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 probabili...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-06-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/3/2/31 |
| _version_ | 1818968157404004352 |
|---|---|
| author | Alireza Khalili Golmankhaneh Arran Fernandez |
| author_facet | Alireza Khalili Golmankhaneh Arran Fernandez |
| author_sort | Alireza Khalili Golmankhaneh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T14:00:14Z |
| format | Article |
| id | doaj.art-2c6784049e9e416fa3797b06ec6d78b3 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-12-20T14:00:14Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-2c6784049e9e416fa3797b06ec6d78b32022-12-21T19:38:23ZengMDPI AGFractal and Fractional2504-31102019-06-01323110.3390/fractalfract3020031fractalfract3020031Random Variables and Stable Distributions on Fractal Cantor SetsAlireza Khalili Golmankhaneh0Arran Fernandez1Young Researchers and Elite Club, Urmia Branch, Islamic Azad University, Urmia 57169-63896, IranDepartment of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Famagusta 99628, TurkeyIn 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.https://www.mdpi.com/2504-3110/3/2/31fractal thin Cantor-like setsfractal random variablefractal Shannon entropyfractal stable distributions |
| spellingShingle | Alireza Khalili Golmankhaneh Arran Fernandez Random Variables and Stable Distributions on Fractal Cantor Sets Fractal and Fractional fractal thin Cantor-like sets fractal random variable fractal Shannon entropy fractal stable distributions |
| title | Random Variables and Stable Distributions on Fractal Cantor Sets |
| title_full | Random Variables and Stable Distributions on Fractal Cantor Sets |
| title_fullStr | Random Variables and Stable Distributions on Fractal Cantor Sets |
| title_full_unstemmed | Random Variables and Stable Distributions on Fractal Cantor Sets |
| title_short | Random Variables and Stable Distributions on Fractal Cantor Sets |
| title_sort | random variables and stable distributions on fractal cantor sets |
| topic | fractal thin Cantor-like sets fractal random variable fractal Shannon entropy fractal stable distributions |
| url | https://www.mdpi.com/2504-3110/3/2/31 |
| work_keys_str_mv | AT alirezakhaliligolmankhaneh randomvariablesandstabledistributionsonfractalcantorsets AT arranfernandez randomvariablesandstabledistributionsonfractalcantorsets |