Probability density function ![]() | |||
Cumulative distribution function ![]() | |||
Parameters |
(real) (real) | ||
---|---|---|---|
Support | |||
CDF | |||
Mean | infinite | ||
Median | |||
Variance | infinite | ||
Skewness | does not exist | ||
Excess kurtosis | does not exist | ||
MGF | does not exist |
In probability theory, a log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If X is a random variable with a Cauchy distribution, then Y = exp(X) has a log-Cauchy distribution; likewise, if Y has a log-Cauchy distribution, then X = log(Y) has a Cauchy distribution.[1]
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