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Autor:
Sibisi, Nomvelo Karabo
This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag-Leffler density, whose Laplace transform is a corresponding Mittag-Le
Externí odkaz:
http://arxiv.org/abs/2402.15228
Autor:
Sibisi, Nomvelo Karabo
This paper combines probability theory and fractional calculus to derive a novel integral representation of the three-parameter Mittag-Leffler function or Prabhakar function, where the three parameters are combinations of four base parameters. The fu
Externí odkaz:
http://arxiv.org/abs/2304.00526
Autor:
Sibisi, Nomvelo Karabo
The main contribution of this paper is the use of probability theory to prove that the three-parameter Mittag-Leffler function is the Laplace transform of a distribution and thus completely monotone. Pollard used contour integration to prove the resu
Externí odkaz:
http://arxiv.org/abs/2301.01466
Autor:
Sibisi, Nomvelo Karabo
Pollard used contour integration to show that the Mittag-Leffler function is the Laplace transform of a positive function, thereby proving that it is completely monotone. He also cited personal communication by Feller of a discovery of the result by
Externí odkaz:
http://arxiv.org/abs/2205.05417