Let Z1, Z2 be two independent, identically distributed random variables whose logarithms are normally distributed. We derive the generating function, expectation, and variance of the logarithm of the sum of Z1 and Z2. The expressions for the expectation and variance involve the sums of rapidly converging series. Converging upper and lower bounds to the expectation are given to indicate the number of terms in the series that need to be evaluated to yield a specified number of significant places.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty