Uses In Bayesian statistics, the log-Cauchy distribution can be used to approximate the improper Jeffreys-Haldane density, 1/k, which is sometimes suggested as the prior distribution for k where k is a positive parameter being estimated. The log-Cauchy distribution can be used to model certain survival processes where significant outliers or extreme results may occur. An example of a process where a log-Cauchy distribution may be an appropriate model is the time between someone becoming infected with HIV and showing symptoms of the disease, which may be very long for some people. It has also been proposed as a model for species abundance patterns. References Continuous distributions Probability distributions with non-finite variance