Cute But Cunning: Circumventing Lognormal Statistic Complexities

Abstract

Though widely used to model various natural phenomena, the lognormal distribution poses significant challenges in mathematical tractability. Its formulation alone is simple, elegant, and easily manageable. But its composition renders this distribution intricate to compute. These challenges hinder straightforward statistical analysis and often necessitate approximations, numerical methods, or simulations for practical use in wireless communications, finance, risk management, etc. In this letter, we aim to ease the analytical intractability of the lognormal distribution by providing asymptotically exact alternative formulations for its probability density function and, through these new formulas, derive some relevant, unprecedented expressions for cumulative distribution function, characteristic function, bit error rate, channel capacity, and composite fading (short-term−long-term).