Lognormal Distribution |
(continuous probability dist. for equations) |
Usage: |
LognormalDist (x, ζ, Φ) |
Definition: |
N (log (x), ζ, Φ) / x = (1 / [x Φ sqrt(2π)]) exp (-[(log(x) - ζ) / Φ]^2 / 2) where N is the normal distribution |
Required: |
Φ > 0 |
Support: |
x > 0 |
Moments: |
μ = exp (ζ + Φ^2 / 2) σ^2 = exp (2ζ + Φ^2) [exp (Φ^2) – 1] γ1 = [exp (Φ^2) + 2] sqrt (exp (Φ^2) – 1) β2 = exp (4 Φ^2) + 2 exp (3 Φ^2) + 3 exp (2 Φ^2) |
The lognormal distribution results when the logarithm of the random variable is described by a normal distribution. This is often the case for a variable which is the product of a number of random variables (by the central limit theorem).
Notice that the ‘n’ of Lognormal is not capitalized, indicating that this is not the same as the logarithm of the normal distribution.