STATISTICAL POWER SUM ANALYSIS FOR NONIDENTICALLY DISTRIBUTED CORRELATED LOGNORMAL SIGNALS

Sum statistics of multiple lognormally distributed correlated random variables are studied in the case of nonidentical means and standard deviations. The FentonWilkinson and Ho’s modification of the Schwartz-Yeh approximation are used as analytical tools. Their accuracy is tested with Monte Carlo simulations. Numerical results show that both approximations fail to match simulation results in the case of nonidentically distributed correlated signals. The Fenton-Wilkinson approximation breaks down if standard deviations are large. The Schwartz-Yeh approximation is quite accurate for the mean and standard deviation statistics for uncorrelated signals. Overall, it seems best to rely on Monte Carlo simulations if the lognormal sum is composed of many heterogeneous correlated components.