# Lognormal Distribution

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Related to Log-normal distribution: Poisson distribution, Gamma distribution, Exponential distribution, Beta distribution, Weibull distribution, Pareto distribution

## lognormal distribution

[′läg‚nȯr·məl ‚di·strə′byü·shən] (statistics)

A probability distribution in which the logarithm of the parameter has a normal distribution.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from

*The Great Soviet Encyclopedia*(1979). It might be outdated or ideologically biased.## Lognormal Distribution

a special type of probability distribution of random variables. If *X* has a normal distribution and if *Y = e ^{x}*, 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

*m _{Y}* =

*e*+

^{m}*σ*

^{2}/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.

### REFERENCES

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.

V. I. BITIUTSKOV

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.