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Log-Shifted Gamma Approximation to Lognormal Sum Distributions
Lam, C.L.J.; Tho Le-Ngoc;
Vehicular Technology, IEEE Transactions on
Volume 56,
Issue 4,
July 2007
Page(s):2121
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2129
Abstract:
This paper proposes the log-shifted gamma (LSG) approximation to model the sum of M lognormally distributed random variables (RVs). The closed-form probability density function of the resulting LSG RV is presented, and its parameters are directly derived from those of the M individual lognormal RVs by using an iterative moment-matching technique without the need for curve fitting of computer-generated distributions. Simulation and analytical results on the cumulative distribution function (cdf) of the sum of M lognormal RVs in different conditions indicate that the proposed LSG approximation can provide better accuracy than other lognormal approximations over a wide cdf range, especially for large M and/or standard deviation.
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