Gibrat's distribution is a continuous distribution in which the logarithm of a variable has a normal distribution ,

(1)

defined over the interval . It is a special case of the log
normal distribution

(2)

with
and ,
and so has distribution function

(3)

The mean , variance , skewness ,
and kurtosis excess are then given by

See also Log Normal Distribution
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References Gibrat, R. Les Inégalités économiques. Paris: Recueil Sirey, 1931. Mansfield, E. "Entry, Gibrat's Law,
Innovation, and the Growth of Firms." Amer. Econ. Rev. 52 , 1023-1051,
1962. Referenced on Wolfram|Alpha Gibrat's Distribution
Cite this as:
Weisstein, Eric W. "Gibrat's Distribution."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/GibratsDistribution.html

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