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.