Reference

density

$h\left(x\right)$

$\psi \left(x\right)$

Student t₃

$\log \left(1+x^2/3\right)$

$\left(x/3\right)/\left(1+x^2/3\right)$

Pearson IV

$m\log \left\{1+\left[{\left(\left(x-\lambda \right)/a\right)}^2\right]\right\}+{\tan }^{-1}\left[\left(x-\lambda \right)/a\right]$

$2m\left[\frac{x-\lambda }{a^2+x^2}\right]+\left[\frac{av}{a^2+x^2}\right]$

Normal

$x^2/2$

X