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A Note on the Characterization of Positive Linnik Laws

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Recently, Jayakumar & Pillai (1996) gave an interesting characterization of the positive Linnik laws in terms of the spectrum function of an infinitely divisible law. This paper improves their result and simplifies their proof. It proves another characterization result in terms of the Pareto law. Further, it represents the positive Linnik random variable as a function of independent gamma random variables.
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Keywords: Laplace transform; Lévy measure; Mittag–Leffler function; Pareto law; characterization; completely monotone function; positive Linnik law; spectrum function

Document Type: Research Article

Affiliations: Institute of Statistical science, Academia Sinica, Republic of China

Publication date: March 1, 2001

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