We present here characterizations of certain families of generalized gamma convolution distributions of L. Bondesson based on a simple relationship between two truncated moments. We also present a list of well-known random variables whose distributions or the distributions of certain functions of them belong to the class of generalized gamma convolutions.
[1] Bondesson L. A general result on infinite divisibility The Annals. of Probability 7 (1979) 965-979.
[2] Bondesson L. Lecture Notes in Statistics Springer-Verlag 1992.
[3] Galambos J. and Kotz S. Characterizations of probability distributions. A unified approach with an emphasis on exponential and related models Lecture Notes in Mathematics 675 Springer Berlin 1978.
[4] Glänzel W. A characterization of the normal distribution Studia Sci. Math.Hungar. 23 (1988) 89 − 91.
[5] Glänzel W. A characterization theorem based on truncated moments and its application to some distribution families Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf 1986) Vol. B Reidel Dordrecht 1987 75 − 84.
[6] Glänzel W. Some consequences of a characterization theorem based on truncated moments Statistics 21 (1990) 613 − 618.
[7] Glänzel W. Ir Win- A characterization tool for discrete distributions under Window( R) Proc. COMPSTAT ’ 94 (Vienna 1994) Short Communications in Computational Statistics ed. by R. Dutter and W. Grossman Vienna 199 − 200.
[8] Glänzel W. Telcs A. and Schubert A. Characterization by truncated moments and its application to Pearson-type distributions Z. Wahrsch. Verw. Gebiete 66 (1984) 173 − 183.
[9] Glänzel W. and Hamedani G.G. Characterizations of univariate continuous distributions Studia Sci. Math. Hungar. 37 (2001) 83 − 118.
[10] Hamedani G.G. Characterizations of Cauchy normal and uniform distributions Studia Sci. Math. Hungar. 28 (1993) 243 − 247.
[11] Hamedani G.G. Characterizations of univariate continuous distributions. II Studia Sci. Math. Hungar. 39 (2002) 407 − 424.
[12] Hamedani G.G. Characterizations of univariate continuous distributions. III Studia Sci. Math. Hungar. 43 (2006) 361 − 385.
[13] Johnson N.I. and Kotz S. Distributions in statistics. Continuous univariate distributions Volumes 1 and 2 Houghton Mifflin Co. Boston Mass. 1970.
[14] Kotz S. and Shanbhag D.N. Some new approaches to probability distributions Adv. in Appl. Probab. 12 (1980) 903 − 921.
[15] Thorin O. On the infinite divisibility of the Pareto distribution Scand. Actuarial J. (1977) 31 − 40.