Highly Accurate Log Skew Normal Approximation to the Sum of Correlated Lognormals

摘要

Several methods have been proposed to approximate the sum of correlatedlognormal RVs. However the accuracy of each method relies highly on the regionof the resulting distribution being examined, and the individual lognormalparameters, i.e., mean and variance. There is no such method which can providethe needed accuracy for all cases. This paper propose a universal yet verysimple approximation method for the sum of correlated lognormals based on logskew normal approximation. The main contribution on this work is to propose ananalytical method for log skew normal parameters estimation. The proposedmethod provides highly accurate approximation to the sum of correlatedlognormal distributions over the whole range of dB spreads for any correlationcoefficient. Simulation results show that our method outperforms all previouslyproposed methods and provides an accuracy within 0.01 dB for all cases.