Fitting the Modified-Power-Lognormal to the Sum of Independent Lognormals Distribution

We propose a new method for calculating a tight approximation to the distribution of the sum of independent lognormal random variables. We make use of a three-parameter modified-power-lognormal distribution function as the approximating distribution. We use theoretical results from our previous work on the tails of the distribution of the sum of lognormals to match the slope of the modified-power-lognormal function at both tails. This would not have been possible with many of the recently-proposed distribution functions, which do not behave properly in the tails. We then also use moment-matching to find the best curve match. Our method is mostly closed-form, requiring only one simple numerical integral. We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method is more accurate than the simple (closed-form) methods, and much simpler to understand and implement than the more accurate methods which rely heavily on numerical integration.