I am looking for the family of distributions that satisfy the following condition:
$\int_{-1}^{+\infty}f(x)x d x=0$
and with this other conditions on $f(x)$:
$f(x)\ge 0 \text{ in }(-1,+\infty]$
$\int_{-1}^{+\infty}f(x) d x =1$
Any idea on how to solve it?