A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION
In this paper, we consider a problem of characterizing distribution through the constructive property of random sumpSN , where 0
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| Veröffentlicht in: | Taiwanese journal of mathematics 2012-08, Vol.16 (4), p.1245-1264 |
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| container_end_page | 1264 |
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| container_issue | 4 |
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| container_title | Taiwanese journal of mathematics |
| container_volume | 16 |
| creator | Hu, Chin-Yuan Cheng, Tsung-Lin |
| description | In this paper, we consider a problem of characterizing distribution through the constructive property of random sumpSN
, where 0 |
| doi_str_mv | 10.11650/twjm/1500406734 |
| format | Article |
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, where 0 <p< 1 andN≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.
2010Mathematics Subject Classification: 621E0.
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, where 0 <p< 1 andN≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.
2010Mathematics Subject Classification: 621E0.
Key words and phrases: Characteristic function, Random summation.</description><subject>Distribution functions</subject><subject>Integers</subject><subject>Mathematical theorems</subject><subject>Probability distributions</subject><subject>Queueing theory</subject><subject>Random variables</subject><subject>Uniqueness</subject><issn>1027-5487</issn><issn>2224-6851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNpFj01Lw0AURQdRMFb3LrN0E_veZDIzXU7T1gaaBvKx0M0wyUywxVJJAuK_t2lFV4_7OPfCIeQR4RmRRzAdvvaHKUYADLgI2RXxKKUs4DLCa-IhUBFETIpbctf3ewAqOXKPCOXHa5WruFzmyZsqk2zrZyt_kRRlnsyrMRf-_NXP1XaRpX5RpekZuic3rfno3cPvnZBqtSzjdbDJXpJYbYImRDkEokYU6OwMmQwNldYy6cZn64yN2AyxkaKWphGSW1oDItgWaueaVhqQJpwQuOw23bHvO9fqz253MN23RtBncT2K63_xU-XpUtn3w7H74wezO4FmeNfINdNIWRT-AN7HVaU</recordid><startdate>20120801</startdate><enddate>20120801</enddate><creator>Hu, Chin-Yuan</creator><creator>Cheng, Tsung-Lin</creator><general>Mathematical Society of the Republic of China</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20120801</creationdate><title>A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION</title><author>Hu, Chin-Yuan ; Cheng, Tsung-Lin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c318t-7b1171ed91483a28dd48e7b11fead54911c87b8ac786d2b0110df0beecf8a08a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Distribution functions</topic><topic>Integers</topic><topic>Mathematical theorems</topic><topic>Probability distributions</topic><topic>Queueing theory</topic><topic>Random variables</topic><topic>Uniqueness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Chin-Yuan</creatorcontrib><creatorcontrib>Cheng, Tsung-Lin</creatorcontrib><collection>CrossRef</collection><jtitle>Taiwanese journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Chin-Yuan</au><au>Cheng, Tsung-Lin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION</atitle><jtitle>Taiwanese journal of mathematics</jtitle><date>2012-08-01</date><risdate>2012</risdate><volume>16</volume><issue>4</issue><spage>1245</spage><epage>1264</epage><pages>1245-1264</pages><issn>1027-5487</issn><eissn>2224-6851</eissn><abstract>In this paper, we consider a problem of characterizing distribution through the constructive property of random sumpSN
, where 0 <p< 1 andN≥ 0 is an integer-valued random variable. This problem will be solved under some regular conditions. We extend the characterization of exponential distribution to a general case. For example, the gamma distribution, the positive Linnik distribution and the scale mixture of stable distribution are characterized. Two new results in the vein are obtained. Finally, the problem of characterizing distribution by the property of the first order statistics is also investigated.
2010Mathematics Subject Classification: 621E0.
Key words and phrases: Characteristic function, Random summation.</abstract><pub>Mathematical Society of the Republic of China</pub><doi>10.11650/twjm/1500406734</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Taiwanese journal of mathematics, 2012-08, Vol.16 (4), p.1245-1264 |
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| language | eng |
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| source | Jstor Complete Legacy; Project Euclid Open Access; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Project Euclid Complete; JSTOR Mathematics & Statistics |
| subjects | Distribution functions Integers Mathematical theorems Probability distributions Queueing theory Random variables Uniqueness |
| title | A CHARACTERIZATION OF DISTRIBUTIONS BY RANDOM SUMMATION |
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