Jones and Faddy Skew-T Distribution

A skew extension of the t distribution, defined for $a>0$ and $b>0$.

where $C_{a,b}=2^{a+b-1}B(a,b)(a+b{)}^{1/2}$, $B$ is the beta function scipy.special.beta and the formula for the moments ${\mu }_n^{\prime }$ holds provided that $a>n/2$ and $b>n/2$.

When $a<b$, the distribution is negatively skewed, and when $a>b$, the distribution is positively skewed. If $a=b$, then we recover the t distribution with $2a$ degrees of freedom.

References

• M.C. Jones and M.J. Faddy. "A skew extension of the t distribution, with applications" Journal of the Royal Statistical Society, Series B (Statistical Methodology) 65, no. 1 (2003): 159-174. 10.1111/1467-9868.00378

Implementation: scipy.stats.jf_skew_t