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单词 lognormal distribution
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Lognormal 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.

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

lognormal distribution


log·nor·mal dis·tri·bu·tion

if a variable y is such that x = log y, it is said to have a lognormal distribution; this is a skew distribution.

Lognormal distribution


Lognormal distribution

Pattern of frequency of occurrence in which the logarithm of the variable follows a normal distribution. Lognormal distributions are used to describe returns calculated over periods of a year or more.

Lognormal Distribution

A way to calculate long-term returns on an investment where the natural log of some variable has a normal distribution.
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