In the case where σ2A=σ2B=σ2 we have then that the expected value is exp[μAσ2+μBσ2+σ2σ2σ2+σ2]=exp[μA+μB+σ22]=√exp[μA+σ2/2]√exp[μB+σ2/2], which is exactly the geometric mean of the expected values of the individual predictions.
I have checked this generalises. If all the lognormals have logarithms whose standard deviation is the same, the mean of the aggregated distribution is the geometric mean of the means of the input distributions.
Thanks, Jaime!
I have checked this generalises. If all the lognormals have logarithms whose standard deviation is the same, the mean of the aggregated distribution is the geometric mean of the means of the input distributions.