Lognormal Distribution

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lognormal distribution

[′läg‚nȯr·məl ‚di·strə′byü·shən]
A probability distribution in which the logarithm of the parameter has a normal distribution.

Lognormal Distribution


a special type of probability distribution of random variables. If X has a normal distribution and if Y = ex, then Y will have a lognormal distribution characterized by the density

Here, m and σ are the parameters of the distribution of the variable X. The mathematical expectation Y is

mY = em + σ2/2

and the dispersion,

The sizes of particles of a crushed material (a rock, for example) and the content of many minerals in rocks obey this distribution to a good approximation.


Kolmogorov, A. N. “O logarifmicheski-normal’nom zakone raspredeleniia razmerov chastits pri droblenii.” Dokl. AN SSSR, 1941, vol. 31, issue 2, pp. 99–101.
Cramer, H. Matematicheskie metody statistiki. Moscow, 1948. (Translated from English.)
Aitchison, J., and J. A. C. Brown. The Lognormal Distribution. Cambridge, 1957.


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