In this paper we consider the distribution
G
(
x
)
=
F
−
1
∫
0
x
(
Γ
(
t
)
)
−
1
d
t
G(x) = {F^{ - 1}}\smallint _0^x{(\Gamma (t))^{ - 1}}\;dt
. The aim of the investigation is twofold: first,to find numerical values of characteristics such as moments, variance, skewness, kurtosis,etc.; second, to study analytically and numerically the moment generating function
φ
(
t
)
=
∫
0
∞
e
−
t
x
/
Γ
(
x
)
d
x
\varphi (t) = \smallint _0^\infty {e^{ - tx}}/\Gamma (x)\;dx
. Furthermore, we also make a generalization of the reciprocal gamma distribution, and study some of its properties.