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.
- Curve of Constant Width
- Curvilinear Coordinates
- Cushion
- Cusp
- Cusp Catastrophe
- Cusp Form
- Cusp Map
- Cusp Point
- Cutting
- Cut-Vertex
- CW-Approximation Theorem
- CW-Complex
- Transfinite Diameter
- Transfinite Number
- Transform
- Transformation
- Transitive
- Transitive Closure
- Transitive Reduction
- Transitivity Class
- Translation
- Translation Relation
- Transpose
- Transpose Map
- Transposition