The Sum and Difference of Two Lognormal Random Variables

Figure 1

Probability density versus 𝑆₁+𝑆₂: The solid lines denote the distributions of the approximate shifted lognormal process, and the dash lines show the exact results. (a) 𝑆₁₀=110, 𝑆₂₀=100, 𝜎₁=0.25, and 𝜎₂=0.15; (b) 𝑆₁₀=110, 𝑆₂₀=70, 𝜎₁=0.25, and 𝜎₂=0.15; (c) 𝑆₁₀=110, 𝑆₂₀=40, 𝜎₁=0.25, and 𝜎₂=0.15; (d) 𝑆₁₀=110, 𝑆₂₀=100, 𝜎₁=0.3, and 𝜎₂=0.2; (e) 𝑆₁₀=110, 𝑆₂₀=70, 𝜎₁=0.3, and 𝜎₂=0.2; (f) 𝑆₁₀=110, 𝑆₂₀=40, 𝜎₁=0.3, and 𝜎₂=0.2.

(a)

(b)

(c)

(d)

(e)

(f)