# Lognormal Distribution

Also found in: Dictionary, Thesaurus, Medical, Legal, Financial.

## 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 It might be outdated or ideologically biased.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 = 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.

### 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

Mentioned in ?
References in periodicals archive ?
Following the same reasoning through a probabilistic approach would have led to 3 lognormal distributions for the [AF.sub.A], [AF.sub.H] and [AF.sub.S], with percentiles ranges of 1([P.sub.0.05])-3([P.sub.0.95]), 1([P.sub.0.05])-10([P.sub.0.95]), and 1([P.sub.0.05])-3([P.sub.0.95]), respectively.
The output of the linear regression analysis, in a logtransformed space and with empirically based limit-state models, maybe used to develop closed-form expressions for fragility functions, assuming limit-state models also follow a lognormal distribution:
Here, we outline the basic steps of the procedure we are proposing for estimating the parameters of the truncated lognormal distribution. To avoid overwhelming the reader with mathematical details, we present the supporting derivations in the "Derivation of the Procedure for Parameter Estimation" and "Equivalence of Maximum Likelihood and Method of Moments Estimates" sections.
We employ Poisson distribution failure model with [lambda]=19 and Lognormal distribution restoration model with [mu]=1, [delta]=0.2.
Then, we obtained statistical simulations of time-dependent responses with normal and lognormal distributions, which were subsequently summarized in order to obtain the statistical distribution of the injury risk.
For the occupancy schedules, the lognormal distribution was used with Equation 3.
Empirical models include negative binomial distribution, log-series distribution, geometric distribution, lognormal distribution and so on.
We further assumed that the incubation periods of cases among humans in all cities followed the same lognormal distribution. The start date of the study time horizon for a given area was either 14 days before the start date of LPM closure or the onset date of the first confirmed local H7N9 case in 2014, whichever was later.
For soil parameters, which show typically a large scatterings (it means those with value of coefficient of variation CoV = S/[bar.X] > 0,3) the lognormal distribution is preferable (Pohl 2011).
In this paper we use a parametric method based on lognormal distribution. We assume, as Melick and Thomas (1997) and Soderlind and Svensson (1997), that RND is some specific parametric function and then we try to find parameters of this function minimizing the differences between option prices in the market and theoretical prices.
The lognormal distribution is given by equation 21:

Site: Follow: Share:
Open / Close