Half-Cauchy distribution

tags

Probability distribution

The half-Cauchy is defined on \(R^+\) and is Cauchy distributed on this domain. It can also be interpreted as a mixture of inverse gamma distributions[]]. In other words:

\begin{equation*} X \sim \operatorname{C}^{+}(0, a) \end{equation*}

is equivalent to

\begin{align*} X^{2} &\sim \operatorname{InverseGamma}(1/2,\, 1/\xi)\\ \xi &\sim \operatorname{InverseGamme}(1/2,\, 1/a^2) \end{align*}