Log Normal Distribution
A Continuous Distribution in which the Logarithm of a variable has a Normal Distribution.It is a general case of Gilbrat's Distribution, to which the log normal distribution reduces with 
and
. The probability density and cumulative distribution functions for the log normal distribution are
 |  |  | (1) |
 | |  | (2) |
where
is the Erf function.This distribution is normalized, since letting 
gives 
and 
, so | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
 | |  | (7) |
These can be found by direct integration
| |  | |
|  | ||
|  | ||
|  | ||
|  | ||
|  | ||
|  | (8) |
and similarly for
. Examples of variates which have approximately log normal distributions include the size ofsilver particles in a photographic emulsion, the survival time of bacteria in disinfectants, the weight and bloodpressure of humans, and the number of words written in sentences by George Bernard Shaw.See also Gilbrat's Distribution, Weibull Distribution
References
Aitchison, J. and Brown, J. A. C. The Lognormal Distribution, with Special Reference to Its Use in Economics. New York: Cambridge University Press, 1957. Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, p. 123, 1951.
- Sibling
- Sicherman Dice
- Sici Spiral
- Side
- Sidon Sequence
- Siegel Disk Fractal
- Siegel Modular Function
- Siegel's Paradox
- Siegel's Theorem
- Sierpinski Arrowhead Curve
- Sierpinski Carpet
- Sierpinski Constant
- Sierpinski Curve
- Sierpinski Gasket
- Sierpinski-Menger Sponge
- Sierpinski Number of the First Kind
- Sierpinski Number of the Second Kind
- Sierpinski's Composite Number Theorem
- Sierpinski Sieve
- Sierpinski Sponge
- Sierpinski's Prime Sequence Theorem
- Sierpinski's Theorem
- Sierpinski Tetrahedron
- Sierpinski Triangle
- Sieve