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Least Squares Approximations to Lognormal Sum Distributions

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2 Author(s)
Lian Zhao ; Dept. of Electr. & Comput. Eng., Ryerson Univ., Toronto, Ont. ; Jiu Ding

In this paper, the least squares (LS) approximation approach is applied to solve the approximation problem of a sum of lognormal random variables (RVs). The LS linear approximation is based on the widely accepted assumption that the sum of lognormal RVs can be approximated by a lognormal RV. We further derive the solution for the LS quadratic (LSQ) approximation, and our results show that the LSQ approximation exhibits an excellent match with the simulation results in a wide range of the distributions of the summands. Using the coefficients obtained from the LSQ method, we present the explicit closed-form expressions of the coefficients as a function of the decibel spread and the number of the summands by applying an LS curve fitting technique. Closed-form expressions for the cumulative distribution function and the probability density function for the sum RV, in both the linear and logarithm domains, are presented

Published in:

IEEE Transactions on Vehicular Technology  (Volume:56 ,  Issue: 2 )