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

Nadhir Ben Rached, Fatma Benkhelifa, Mohamed-Slim Alouini, Raul Tempone

Research output: Chapter in Book/Report/Conference proceedingConference proceedingpeer-review

9 Citations (Scopus)


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.
Original languageEnglish
Title of host publication IEEE International Conference on Communications (ICC)
Number of pages6
ISBN (Electronic)978-1-4673-6432-4
Publication statusPublished - 10 Sept 2015
Externally publishedYes
Event2015 IEEE International Conference on Communications (ICC) - London, United Kingdom
Duration: 8 Jun 201512 Jun 2015


Conference2015 IEEE International Conference on Communications (ICC)
Country/TerritoryUnited Kingdom


  • Hazards
  • Least squares approximations
  • Monte Carlo methods
  • Computational modeling
  • Random variables
  • Tin


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