A fast simulation method for the Log-normal sum distribution using a hazard rate twisting technique

Handle URI:
http://hdl.handle.net/10754/578800
Title:
A fast simulation method for the Log-normal sum distribution using a hazard rate twisting technique
Authors:
Rached, Nadhir B.; Benkhelifa, Fatma; Alouini, Mohamed-Slim ( 0000-0003-4827-1793 ) ; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
The probability density function of the sum of Log-normally distributed random variables (RVs) is a well-known challenging problem. For instance, an analytical closed-form expression of the Log-normal sum distribution does not exist and is still an open problem. A crude Monte Carlo (MC) simulation is of course an alternative approach. However, this technique is computationally expensive especially when dealing with rare events (i.e. events with very small probabilities). Importance Sampling (IS) is a method that improves the computational efficiency of MC simulations. In this paper, we develop an efficient IS method for the estimation of the Complementary Cumulative Distribution Function (CCDF) of the sum of independent and not identically distributed Log-normal RVs. This technique is based on constructing a sampling distribution via twisting the hazard rate of the original probability measure. Our main result is that the estimation of the CCDF is asymptotically optimal using the proposed IS hazard rate twisting technique. We also offer some selected simulation results illustrating the considerable computational gain of the IS method compared to the naive MC simulation approach.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2015 IEEE International Conference on Communications (ICC)
Conference/Event name:
IEEE International Conference on Communications, ICC 2015
Issue Date:
8-Jun-2015
DOI:
10.1109/ICC.2015.7248992
Type:
Conference Paper
Additional Links:
http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7248992
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorRached, Nadhir B.en
dc.contributor.authorBenkhelifa, Fatmaen
dc.contributor.authorAlouini, Mohamed-Slimen
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-09-28T08:07:06Zen
dc.date.available2015-09-28T08:07:06Zen
dc.date.issued2015-06-08en
dc.identifier.doi10.1109/ICC.2015.7248992en
dc.identifier.urihttp://hdl.handle.net/10754/578800en
dc.description.abstractThe probability density function of the sum of Log-normally distributed random variables (RVs) is a well-known challenging problem. For instance, an analytical closed-form expression of the Log-normal sum distribution does not exist and is still an open problem. A crude Monte Carlo (MC) simulation is of course an alternative approach. However, this technique is computationally expensive especially when dealing with rare events (i.e. events with very small probabilities). Importance Sampling (IS) is a method that improves the computational efficiency of MC simulations. In this paper, we develop an efficient IS method for the estimation of the Complementary Cumulative Distribution Function (CCDF) of the sum of independent and not identically distributed Log-normal RVs. This technique is based on constructing a sampling distribution via twisting the hazard rate of the original probability measure. Our main result is that the estimation of the CCDF is asymptotically optimal using the proposed IS hazard rate twisting technique. We also offer some selected simulation results illustrating the considerable computational gain of the IS method compared to the naive MC simulation approach.en
dc.language.isoenen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7248992en
dc.rights(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.subjectCrude Monte Carloen
dc.subjectHazard rate twistingen
dc.subjectImportance Samplingen
dc.subjectLog-normal sum distributionen
dc.subjectRare eventsen
dc.titleA fast simulation method for the Log-normal sum distribution using a hazard rate twisting techniqueen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2015 IEEE International Conference on Communications (ICC)en
dc.conference.date2015-06-08 to 2015-06-12en
dc.conference.nameIEEE International Conference on Communications, ICC 2015en
dc.conference.locationLondon, GBRen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorBenkhelifa, Fatmaen
kaust.authorAlouini, Mohamed-Slimen
kaust.authorTempone, Raulen
kaust.authorRached, Nadhir B.en
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