Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables
We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applie...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/630857 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849402952055259136 |
|---|---|
| author | Xin Gao Hong Xu Dong Ye |
| author_facet | Xin Gao Hong Xu Dong Ye |
| author_sort | Xin Gao |
| collection | DOAJ |
| description | We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with more than two lognormally distributed random variables under some stricter conditions. The results yield new insights into the problem of characterization for a sum of lognormally distributed random variables and demonstrate that there is a need to revisit many existing approximation methods. |
| format | Article |
| id | doaj-art-98753eb02e5f40daa01acf8103775cce |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-98753eb02e5f40daa01acf8103775cce2025-08-20T03:37:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/630857630857Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal VariablesXin Gao0Hong Xu1Dong Ye2Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, CanadaDepartment of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, CanadaLMAM, Université de Metz, UFR 7122 Bâtiment A, Île de Saulcy, 57045 Metz Cedex 1, FranceWe consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with more than two lognormally distributed random variables under some stricter conditions. The results yield new insights into the problem of characterization for a sum of lognormally distributed random variables and demonstrate that there is a need to revisit many existing approximation methods.http://dx.doi.org/10.1155/2009/630857 |
| spellingShingle | Xin Gao Hong Xu Dong Ye Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables |
| title_full | Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables |
| title_fullStr | Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables |
| title_full_unstemmed | Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables |
| title_short | Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables |
| title_sort | asymptotic behavior of tail density for sum of correlated lognormal variables |
| url | http://dx.doi.org/10.1155/2009/630857 |
| work_keys_str_mv | AT xingao asymptoticbehavioroftaildensityforsumofcorrelatedlognormalvariables AT hongxu asymptoticbehavioroftaildensityforsumofcorrelatedlognormalvariables AT dongye asymptoticbehavioroftaildensityforsumofcorrelatedlognormalvariables |