Lognormal Distribution |
(continuous probability dist. for equations) |
Usage: |
LognormalDist (x, x, f) |
Definition: |
N (log (x), x, f) / x = (1 / [x f sqrt(2p)]) exp (-[(log(x) - x) / f]^2 / 2) where N is the normal distribution |
Required: |
f > 0 |
Support: |
x > 0 |
Moments: |
m = exp (x + f^2 / 2) s^2 = exp (2x + f^2) [exp (f^2) – 1] g1 = [exp (f^2) + 2] sqrt (exp (f^2) – 1) b2 = exp (4 f^2) + 2 exp (3 f^2) + 3 exp (2 f^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 = 4 && typeof(BSPSPopupOnMouseOver) == 'function') BSPSPopupOnMouseOver(event);" class="BSSCPopup" onclick="BSSCPopup('X_PU_central_limit_theorem.htm');return false;">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.