TY - GEN

T1 - A fast simulation method for the Log-normal sum distribution using a hazard rate twisting technique

AU - Rached, Nadhir B.

AU - Benkhelifa, Fatma

AU - Alouini, Mohamed-Slim

AU - Tempone, Raul

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2015/9/11

Y1 - 2015/9/11

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/578800

UR - http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7248992

UR - http://www.scopus.com/inward/record.url?scp=84953790316&partnerID=8YFLogxK

U2 - 10.1109/ICC.2015.7248992

DO - 10.1109/ICC.2015.7248992

M3 - Conference contribution

SN - 9781467364324

SP - 4259

EP - 4264

BT - 2015 IEEE International Conference on Communications (ICC)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -