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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Szyszkowicz, S.S. Yanikomeroglu, H. |
| Copyright Year | 2007 |
| Description | Author affiliation: Carleton Univ. Ottawa, Ottawa (Szyszkowicz, S.S.; Yanikomeroglu, H.) |
| Abstract | Finding the distribution of the sum of lognormal random variables is an important mathematical problem in wireless communications, as well as in many other fields. While several methods exist to approximate this distribution, their performance tends to deteriorate in both tails. Finding a good overall fit remains an open problem. Other disadvantages of these methods are their complexity and, in some cases, their limitation to particular scenarios. In this paper we examine the sum of independent lognormal random variables with arbitrary parameters. We define the concept of best lognormal fit to a tail and show what it means in terms of convergence. We restate a known result about asymptotes to the higher tail of the distribution. To our knowledge, the lower tail has not yet been studied. We give a simple closed-form expression for an asymptote to the lower tail. We also show that known methods for finding the sum of lognormals use distribution functions that do not have this asymptotic behaviour in the tails. Our results are complementary to the existing knowledge, which together can combine to solve the problem of the sum of lognormals simply and exactly. We support our results by simulations. |
| Starting Page | 5324 |
| Ending Page | 5329 |
| File Size | 548782 |
| Page Count | 6 |
| File Format | |
| ISBN | 1424403537 |
| DOI | 10.1109/ICC.2007.881 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2007-06-24 |
| Publisher Place | UK |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Probability distribution Tail Distribution functions Random variables Wireless communication Statistical distributions Interference Communications Society Distributed computing Systems engineering and theory |
| Content Type | Text |
| Resource Type | Article |
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