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Mathematics of Computation

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Calculation of the moments and the moment generating function for the reciprocal gamma distribution

Authors: Arne Fransén and Staffan Wrigge
Journal: Math. Comp. 42 (1984), 601-616
MSC: Primary 65D20; Secondary 60E10, 62E15, 65U05
MathSciNet review: 736456
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Abstract: In this paper we consider the distribution $G(x) = {F^{ - 1}}\smallint _0^x{(\Gamma (t))^{ - 1}}\;dt$. 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 $\varphi (t) = \smallint _0^\infty {e^{ - tx}}/\Gamma (x)\;dx$. Furthermore, we also make a generalization of the reciprocal gamma distribution, and study some of its properties.

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Keywords: Reciprocal gamma distribution, population characteristics, generating function
Article copyright: © Copyright 1984 American Mathematical Society