Probability density function
Some log-normal density functions with identical location parameter but differing scale parameters |
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Cumulative distribution function
Cumulative distribution function of the log-normal distribution (with ) |
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Notation | |
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Parameters |
— location, — scale of associated normal |
Support | |
CDF | |
Mean | |
Median | |
Mode | |
Variance | |
Skewness | |
Ex. kurtosis | |
Entropy | |
MGF | defined only on the negative half-axis, see text |
CF | representation is asymptotically divergent but sufficient for numerical purposes |
Fisher information |
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Likewise, if has a normal distribution, then has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution also has been associated with other names, such as McAlister, Gibrat and Cobb–Douglas.