Description

A random variable possesses a Cauchy distribution, if it is continuous, and its density function has the form , . Tails of this distribution are very heavy, not a single moment does exists, even expectation.

The following picture shows graphs of the density function (bound to the left axis) and CDF (bound to the right axis) of Cauchy distribution.

Characteristics

The following picture contains formulae for calculation of characteristics of Cauchy distribution.

Density function
CDF
Expectation	Does not exist
Standard deviation	Does not exist
Variance	Does not exist
Asymmetry	Does not exist
Kurtosis	Does not exist
Median	0
Mode	0