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On the Mittag–Leffler distributions

✍ Scribed by Gwo Dong Lin

Book ID: 104340692
Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 86 KB
Volume: 74
Category: Article
ISSN: 0378-3758
DOI: 10.1016/s0378-3758(98)00096-2

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✦ Synopsis

We ÿrst prove that the Mittag-Le er distributions belong to the class of distributions with complete monotone derivative. Then we investigate the fundamental properties of the Mittag-Le er distributions and of their extensions, including the tail behavior of distribution, the explicit expressions for moments of all orders and for the density functions. The latter has been used to correct some inverse Laplace transforms given in the literature. As a by-product, the moments of negative (integral) orders are used to characterize the positive stable distributions with exponent ∈ [ 1 3 ; 1].

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