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Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables
For a fixed integer n ≥ 2, let X 1 , …, X n be independent random variables (r.v.s) with distributions F 1 ,…, F n , respectively. Let Y be another random variable with distribution G belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. Whe...
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| Published in: | Lithuanian mathematical journal 2012, Vol.52 (1), p.29-39 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c288t-2a15c27d4cb10961934aa3ee8fb52ef657cf8e5445d7300fc3d74d5ee3e3055a3 |
| container_end_page | 39 |
| container_issue | 1 |
| container_start_page | 29 |
| container_title | Lithuanian mathematical journal |
| container_volume | 52 |
| creator | Cheng, Dongya Wang, Yuebao |
| description | For a fixed integer
n
≥ 2, let
X
1
,
…,
X
n
be independent random variables (r.v.s) with distributions
F
1
,…,
F
n
, respectively. Let
Y
be another random variable with distribution
G
belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each tail of
F
i
,
i
= 1
,
…,
n
, is asymptotically less than or equal to the tail of
G
, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum
X
1
+ ⋯ +
X
n
and
Y
. By taking different
G
’s, we obtain general forms of some existing results. |
| doi_str_mv | 10.1007/s10986-012-9153-9 |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s10986_012_9153_9</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s10986_012_9153_9</sourcerecordid><originalsourceid>FETCH-LOGICAL-c288t-2a15c27d4cb10961934aa3ee8fb52ef657cf8e5445d7300fc3d74d5ee3e3055a3</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EEqXwAez8AwY_4sRZVhUvqRIbWFuOPaaukjiy04r-PS5lzWYeV3NHMwehe0YfGKXNY2a0VTWhjJOWSUHaC7RgshFEKS4v0YKKWhBWN_wa3eS8o7SMM7pAYZWPwzTHOVjcwdYcQkw4ejxvASczh_jbmNDjKcXOdKEPc4B8UvN-wGZ0eDDfYSh1kcLoYIISxrm4RxcHfDApmK6HfIuuvOkz3P3lJfp8fvpYv5LN-8vberUhlis1E26YtLxxle3KSzVrRWWMAFC-kxx8LRvrFciqkq4RlHorXFM5CSBAUCmNWCJ23mtTzDmB11MKg0lHzag-sdJnVrqw0idWui0efvbkMjt-QdK7uE9jOfMf0w9yU26E</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables</title><source>Springer Nature</source><creator>Cheng, Dongya ; Wang, Yuebao</creator><creatorcontrib>Cheng, Dongya ; Wang, Yuebao</creatorcontrib><description>For a fixed integer
n
≥ 2, let
X
1
,
…,
X
n
be independent random variables (r.v.s) with distributions
F
1
,…,
F
n
, respectively. Let
Y
be another random variable with distribution
G
belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each tail of
F
i
,
i
= 1
,
…,
n
, is asymptotically less than or equal to the tail of
G
, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum
X
1
+ ⋯ +
X
n
and
Y
. By taking different
G
’s, we obtain general forms of some existing results.</description><identifier>ISSN: 0363-1672</identifier><identifier>EISSN: 1573-8825</identifier><identifier>DOI: 10.1007/s10986-012-9153-9</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Actuarial Sciences ; Mathematics ; Mathematics and Statistics ; Number Theory ; Ordinary Differential Equations ; Probability Theory and Stochastic Processes</subject><ispartof>Lithuanian mathematical journal, 2012, Vol.52 (1), p.29-39</ispartof><rights>Springer Science+Business Media, Inc. 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-2a15c27d4cb10961934aa3ee8fb52ef657cf8e5445d7300fc3d74d5ee3e3055a3</citedby><cites>FETCH-LOGICAL-c288t-2a15c27d4cb10961934aa3ee8fb52ef657cf8e5445d7300fc3d74d5ee3e3055a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Cheng, Dongya</creatorcontrib><creatorcontrib>Wang, Yuebao</creatorcontrib><title>Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables</title><title>Lithuanian mathematical journal</title><addtitle>Lith Math J</addtitle><description>For a fixed integer
n
≥ 2, let
X
1
,
…,
X
n
be independent random variables (r.v.s) with distributions
F
1
,…,
F
n
, respectively. Let
Y
be another random variable with distribution
G
belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each tail of
F
i
,
i
= 1
,
…,
n
, is asymptotically less than or equal to the tail of
G
, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum
X
1
+ ⋯ +
X
n
and
Y
. By taking different
G
’s, we obtain general forms of some existing results.</description><subject>Actuarial Sciences</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number Theory</subject><subject>Ordinary Differential Equations</subject><subject>Probability Theory and Stochastic Processes</subject><issn>0363-1672</issn><issn>1573-8825</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwAez8AwY_4sRZVhUvqRIbWFuOPaaukjiy04r-PS5lzWYeV3NHMwehe0YfGKXNY2a0VTWhjJOWSUHaC7RgshFEKS4v0YKKWhBWN_wa3eS8o7SMM7pAYZWPwzTHOVjcwdYcQkw4ejxvASczh_jbmNDjKcXOdKEPc4B8UvN-wGZ0eDDfYSh1kcLoYIISxrm4RxcHfDApmK6HfIuuvOkz3P3lJfp8fvpYv5LN-8vberUhlis1E26YtLxxle3KSzVrRWWMAFC-kxx8LRvrFciqkq4RlHorXFM5CSBAUCmNWCJ23mtTzDmB11MKg0lHzag-sdJnVrqw0idWui0efvbkMjt-QdK7uE9jOfMf0w9yU26E</recordid><startdate>2012</startdate><enddate>2012</enddate><creator>Cheng, Dongya</creator><creator>Wang, Yuebao</creator><general>Springer US</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>2012</creationdate><title>Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables</title><author>Cheng, Dongya ; Wang, Yuebao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-2a15c27d4cb10961934aa3ee8fb52ef657cf8e5445d7300fc3d74d5ee3e3055a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Actuarial Sciences</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number Theory</topic><topic>Ordinary Differential Equations</topic><topic>Probability Theory and Stochastic Processes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cheng, Dongya</creatorcontrib><creatorcontrib>Wang, Yuebao</creatorcontrib><collection>CrossRef</collection><jtitle>Lithuanian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cheng, Dongya</au><au>Wang, Yuebao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables</atitle><jtitle>Lithuanian mathematical journal</jtitle><stitle>Lith Math J</stitle><date>2012</date><risdate>2012</risdate><volume>52</volume><issue>1</issue><spage>29</spage><epage>39</epage><pages>29-39</pages><issn>0363-1672</issn><eissn>1573-8825</eissn><abstract>For a fixed integer
n
≥ 2, let
X
1
,
…,
X
n
be independent random variables (r.v.s) with distributions
F
1
,…,
F
n
, respectively. Let
Y
be another random variable with distribution
G
belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each tail of
F
i
,
i
= 1
,
…,
n
, is asymptotically less than or equal to the tail of
G
, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum
X
1
+ ⋯ +
X
n
and
Y
. By taking different
G
’s, we obtain general forms of some existing results.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10986-012-9153-9</doi><tpages>11</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0363-1672 |
| ispartof | Lithuanian mathematical journal, 2012, Vol.52 (1), p.29-39 |
| issn | 0363-1672 1573-8825 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s10986_012_9153_9 |
| source | Springer Nature |
| subjects | Actuarial Sciences Mathematics Mathematics and Statistics Number Theory Ordinary Differential Equations Probability Theory and Stochastic Processes |
| title | Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables |
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