Analytic and asymptotic properties of non-symmetric Linnik's probability densities
| dc.citation.epage | 544 | en_US |
| dc.citation.issueNumber | 6 | en_US |
| dc.citation.spage | X | en_US |
| dc.citation.volumeNumber | 5 | en_US |
| dc.contributor.author | Erdoǧan, M.B. | en_US |
| dc.date.accessioned | 2016-02-08T10:40:04Z | |
| dc.date.available | 2016-02-08T10:40:04Z | |
| dc.date.issued | 1999 | en_US |
| dc.department | Department of Mathematics | en_US |
| dc.description.abstract | The function φθα(t) =1/1 + e-iθsgnt|t|α, α ε (0, 2), θ ε (-π, π], is a characteristic function of a probability distribution iff |θ| ≤ min(πα/2, π - πα/2). This distribution is absolutely continuous; for θ = 0 it is symmetric. The latter case was introduced by Linnik in 1953 [13] and several applications were found later. The case θ ≠ 0 was introduced by Klebanov, Maniya, and Melamed in 1984 [9], while some special cases were considered previously by Laha [12] and Pillai [18]. In 1994, Kotz, Ostrovskii and Hayfavi [10] carried out a detailed investigation of analytic and asymptotic properties of the density of the distribution for the symmetric case θ = 0. We generalize their results to the non-symmetric case θ ≠ 0. As in the symmetric case, the arithmetical nature of the parameter a plays an important role, but several new phenomena appear. | en_US |
| dc.identifier.issn | 10695869 | |
| dc.identifier.uri | http://hdl.handle.net/11693/25154 | |
| dc.language.iso | English | en_US |
| dc.source.title | Journal of Fourier Analysis and Applications | en_US |
| dc.subject | Cauchy type integral | en_US |
| dc.subject | Characteristic function | en_US |
| dc.subject | Completely monotonicity | en_US |
| dc.subject | Liouville numbers | en_US |
| dc.subject | Plemelj-Sokhotskii formula | en_US |
| dc.subject | Unimodality | en_US |
| dc.title | Analytic and asymptotic properties of non-symmetric Linnik's probability densities | en_US |
| dc.type | Article | en_US |
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