On Free Generalized Inverse Gaussian Distributions
We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and m...
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| Veröffentlicht in: | Complex analysis and operator theory 2019-10, Vol.13 (7), p.3091-3116 |
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| container_title | Complex analysis and operator theory |
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| creator | Hasebe, Takahiro Szpojankowski, Kamil |
| description | We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables
X
,
Y
where
Y
has a free Poisson distribution one has
X
=
d
1
X
+
Y
if and only if
X
has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy. |
| doi_str_mv | 10.1007/s11785-018-0790-9 |
| format | Article |
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X
,
Y
where
Y
has a free Poisson distribution one has
X
=
d
1
X
+
Y
if and only if
X
has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.</description><identifier>ISSN: 1661-8254</identifier><identifier>EISSN: 1661-8262</identifier><identifier>DOI: 10.1007/s11785-018-0790-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Entropy ; Generalized inverse ; Inverse Gaussian probability distribution ; Mathematics ; Mathematics and Statistics ; Normal distribution ; Operator Theory ; Random variables</subject><ispartof>Complex analysis and operator theory, 2019-10, Vol.13 (7), p.3091-3116</ispartof><rights>The Author(s) 2018</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c469t-baddb751260eb4cd0400be752743aaa5e98d61726721de862192cf4e3136f4cd3</citedby><cites>FETCH-LOGICAL-c469t-baddb751260eb4cd0400be752743aaa5e98d61726721de862192cf4e3136f4cd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11785-018-0790-9$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11785-018-0790-9$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Hasebe, Takahiro</creatorcontrib><creatorcontrib>Szpojankowski, Kamil</creatorcontrib><title>On Free Generalized Inverse Gaussian Distributions</title><title>Complex analysis and operator theory</title><addtitle>Complex Anal. Oper. Theory</addtitle><description>We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables
X
,
Y
where
Y
has a free Poisson distribution one has
X
=
d
1
X
+
Y
if and only if
X
has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.</description><subject>Analysis</subject><subject>Entropy</subject><subject>Generalized inverse</subject><subject>Inverse Gaussian probability distribution</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Normal distribution</subject><subject>Operator Theory</subject><subject>Random variables</subject><issn>1661-8254</issn><issn>1661-8262</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp1kE1Lw0AQhhdRsFZ_gLeA59WZTbIfR6m2Fgq96HnZJBNJqZu6mwj6690S0ZOnGYbnfQcexq4RbhFA3UVEpUsOqDkoA9ycsBlKiVwLKU5_97I4Zxcx7gBkwsyMia3PloEoW5Gn4PbdFzXZ2n9QiOnmxhg757OHLg6hq8ah6328ZGet20e6-plz9rJ8fF488c12tV7cb3hdSDPwyjVNpUoUEqgq6gYKgIpUKVSRO-dKMrqRqIRUAhvSUqARdVtQjrlsE5_P2c3Uewj9-0hxsLt-DD69tCIHqUHpAhKFE1WHPsZArT2E7s2FT4tgj2rspMYmNfaoxpqUEVMmJta_Uvhr_j_0DckHZS8</recordid><startdate>20191001</startdate><enddate>20191001</enddate><creator>Hasebe, Takahiro</creator><creator>Szpojankowski, Kamil</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191001</creationdate><title>On Free Generalized Inverse Gaussian Distributions</title><author>Hasebe, Takahiro ; Szpojankowski, Kamil</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c469t-baddb751260eb4cd0400be752743aaa5e98d61726721de862192cf4e3136f4cd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Analysis</topic><topic>Entropy</topic><topic>Generalized inverse</topic><topic>Inverse Gaussian probability distribution</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Normal distribution</topic><topic>Operator Theory</topic><topic>Random variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hasebe, Takahiro</creatorcontrib><creatorcontrib>Szpojankowski, Kamil</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Complex analysis and operator theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hasebe, Takahiro</au><au>Szpojankowski, Kamil</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Free Generalized Inverse Gaussian Distributions</atitle><jtitle>Complex analysis and operator theory</jtitle><stitle>Complex Anal. Oper. Theory</stitle><date>2019-10-01</date><risdate>2019</risdate><volume>13</volume><issue>7</issue><spage>3091</spage><epage>3116</epage><pages>3091-3116</pages><issn>1661-8254</issn><eissn>1661-8262</eissn><abstract>We study here properties of free Generalized Inverse Gaussian distributions (fGIG) in free probability. We show that in many cases the fGIG shares similar properties with the classical GIG distribution. In particular we prove that fGIG is freely infinitely divisible, free regular and unimodal, and moreover we determine which distributions in this class are freely selfdecomposable. In the second part of the paper we prove that for free random variables
X
,
Y
where
Y
has a free Poisson distribution one has
X
=
d
1
X
+
Y
if and only if
X
has fGIG distribution for special choice of parameters. We also point out that the free GIG distribution maximizes the same free entropy functional as the classical GIG does for the classical entropy.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11785-018-0790-9</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Analysis Entropy Generalized inverse Inverse Gaussian probability distribution Mathematics Mathematics and Statistics Normal distribution Operator Theory Random variables |
| title | On Free Generalized Inverse Gaussian Distributions |
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