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) |
(3) |
(4) | |||
(5) | |||
(6) | |||
(7) |
(8) |
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.
© 1996-9 Eric W. Weisstein