Occasionally, there is a need to evaluate E

X−1

. Piegorsch and Casella (1985)14 have shown that, if X has a continuous density fX (x) with support S = (0,∞), then a sufficient condition for the existence of E

X−1

is

for some r > 0. Under the same conditions, Hannan (1985) showed that

for some r > 1 is also sufficient for the existence of E
X−1
.
Let Z ∼ Gam (α, β). For what α does E
Z−1
exist?

lim fx (x) x-0+x" 8