A Note on the Characterization of Positive Linnik Laws |
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| Authors: | Gwo Dong Lin |
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| Affiliation: | Institute of Statistical science, Academia Sinica, Republic of China |
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| Abstract: | 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: | characterization completely monotone function Laplace transform Lévy measure Mittag–Leffler function Pareto law positive Linnik law spectrum function. |
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