We prove that the distribution of the sum of N identically distributed jointly lognormal random variables, where all pairs have the same strictly positive correlation coefficient, converges to a lognormal with known parameters as N becomes large. We confirm our theorem by simulations and give an application of the theorem. Copyright

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Persistent URL dx.doi.org/10.1109/TCOMM.2009.12.070539
Journal IEEE Transactions on Communications
Szyszkowicz, S.S. (Sebastian S.), & Yanikomeroglu, H. (2009). Limit theorem on the sum of identically distributed equally and positively correlated joint lognormals. IEEE Transactions on Communications, 57(12), 3538–3542. doi:10.1109/TCOMM.2009.12.070539