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Generating the generalized distributions by using fractional calculus | ||
| Journal of Hyperstructures | ||
| دوره 5، شماره 2، اسفند 2016، صفحه 141-150 اصل مقاله (255.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2016.2675 | ||
| نویسندگان | ||
| Masoud Ganji* 1؛ Fatemeh Gharari2 | ||
| 1Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, Iran | ||
| 2Department of Statistics, University of University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabili, Iran | ||
| چکیده | ||
| In this paper, we generalized some statistical distribu- tions by using fractional calculus. The domain of parameter space for these distributions was expanded and their PDFs also presented as a product of fractional derivation of Dirac delta function of shape parameter order. | ||
| کلیدواژه‌ها | ||
| Fractional calculus؛ Dirac delta function؛ Burr distribution؛ Beta type II distribution؛ Beta type III distribution | ||
| مراجع | ||
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[1] M. Ganji, N. Eghbali and F. Gharari, Some Fractional Special Functions and Fractional Moments, Gen. Math. Notes. 18(2)(2013) 120-127. [2] M. Ganji and F. Gharari, The Generalized Fourier Transform for the Generation of Complex Fractional Moments, International Journal of Mathematical Archive (IJMA), 5(1)(2014) 293-299. [3] M. Ganji and F. Gharari, The Generalized Random Variable Appears the Trace of Fractional Calculus in Statistics, Applied Mathematics Information Sciences Letters, 3 (2)(2015) 61-67. [4] R. Hilfer, Threefold introduction to fractional derivatives, Wiley-VCH, Weinheim, (2008). [5] A. Kilbas, M. H. Srivastava and J. J. Trujillo, Theory and Application of Frac-tional Differential Equations, North Holland Mathematics Studies 204, (2006). [6] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Frac-tional Differential Equations, John Wiley and Sons, New York, (1993). [7] K. Oldham and J. Spanier The Fractional Calculus, Theory and Application of Differentiation and Integration to Arbitrary Orders, Academic Press, San Diego, CF,(1974). [8] I. Podlubny, Fractional differential equations, San Diego: Academic Press,(1999). | ||
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