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

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736456-3

MathSciNet review:
736456

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Abstract: In this paper we consider the distribution . 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 . Furthermore, we also make a generalization of the reciprocal gamma distribution, and study some of its properties.

**[1]**J. J. Dorning, B. Nicolaenko & J. K. Thurber, "An integral identity due to Ramanujan which occurs in neutron transport theory,"*J. Math. Mech.*, v. 19, No. 5, 1969, pp. 429-438. MR**0254298 (40:7507)****[2]**A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi,*Higher Transcendental Functions*, Vol. Ill, McGraw-Hill, New York, 1955.**[3]**A. Fransén, Addendum and Corrigendum to "High-precision values of the gamma function and of some related coefficients,"*Math. Comp.*, v. 37, 1981, pp. 233-235. MR**616377 (82m:65002)****[4]**A. Fransén & S. Wrigge, "High-precision values of the gamma function and of some related coefficients,"*Math. Comp.*, v. 34, 1980, pp. 553-566. MR**559204 (81f:65004)****[5]**W. Gautschi, "Polynomials orthogonal with respect to the reciprocal gamma function,"*BIT*, v. 22, 1982, pp. 387-389. MR**675673 (84h:65024)****[6]**G. H. Golub & J. H. Welsch, "Calculation of Gauss quadrature rules,"*Math. Comp.*, v. 23, 1969, pp. 221-230, Microfiche supplement A1-A10. MR**0245201 (39:6513)****[7]**S. A. Gustafson, "Rapid computation of general interpolation formulas and mechanical quadrature rules,"*Comm. ACM*, v. 14, 1971, pp. 797-801, Algorithm 417, p. 807. MR**0311069 (46:10167a)****[8]**G. H. Hardy,*Ramanujan--Twelve Lectures on Subjects Suggested by His Life and Work*, (reprinted), Chelsea, New York, 1959.**[9]**Collected papers of G. H. Hardy, Vols. I-VII (Especially Vol. IV, pp. 544-548), Oxford at the Clarendon Press, 1969.**[10]**W. A. Johnson, Private communication, 1982.**[11]**A. Lindhagen,*Studier öfver Gamma-Funktionen och Några Beslägtade Transcendenter*(Studies of the gamma function and of some related transcendental), Doctoral Thesis, B. Almqvist & J. Wiksell's boktryckeri, Upsala, 1887.**[12]**W. F. Lunnon, P. A. B. Pleasants and N. M. Stephens, "Arithmetic properties of Bell numbers to a composite modulus I,"*Acta Arith.*, v. 35, 1979, pp. 1-16. MR**536875 (80k:05006)****[13]**R. E. A. C. Paley & N. Wiener,*Fourier Transforms in the Complex Domain*, Amer. Math. Soc., New York, 1934. MR**1451142 (98a:01023)****[14]**J. Riordan,*Combinatorial Identities*, Wiley, New York, 1968. MR**0231725 (38:53)****[15]**I. N. Sneddon,*Special Functions of Mathematical Physics and Chemistry*, Oliver and Boyd, Edinburgh and London, 1961. MR**0080170 (18:204a)****[16]**S. Wrigge, "A note on the moment generating function for the reciprocal gamma distribution,"*Math. Comp.*, v. 42, 1984, pp. 617-621. MR**736457 (86f:65042b)****[17]**M. Wyman & R. Wong, "The asymptotic behaviour of ,"*Canad. J. Math.*, v. 21, 1969, pp. 1013-1023. MR**0244521 (39:5835)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736456-3

Keywords:
Reciprocal gamma distribution,
population characteristics,
generating function

Article copyright:
© Copyright 1984
American Mathematical Society