[1]    Barndorff-Nielsen, O. E. and Halgreen, C. (1977). Infinite divisibility of the Hyperbolic and generalized inverse Gaussian distribution. Z. Wahrsch. Verw. Geb. 38, 309–312. MR0436260

[2]    Barndorff-Nielsen, O. E. and Koudou, A. E. (1998). Trees with random conductivities and the (reciprocal) inverse Gaussian distribution. Adv. Appl. Probab. 30, 409–424. MR1642846

[3]    Bernadac, E. (1995). Random continued fractions and inverse Gaussian distribution on a symmetric cone. J. Theor. Probab. 8, 221–260. MR1325851

[4]    Brown, T. and Phillips, M. (1999). Negative binomial approximation with Stein’s method. Methodol. Comput. Appl. Probab. 1, 407–421. MR1770372

[5]    Chatterjee, S., Fulman, S. and Röllin, A. (2011). Exponential approximation by Stein’s method and spectral graph theory. ALEA Lat. Am. J. Probab. Math. Stat. 8, 197–223. MR2802856

[6]    Chebana, F., El Adlouni, S. and Bobée, B. (2010). Mixed estimation methods for Halphen distributions with applications in extreme hydrologic events. Stoch. Environ. Res. Risk Assess. 24, 359–376.

[7]    Chen, L. H. Y. (1975). Poisson approximation for dependent trials. Ann. Probab. 3, 534–545.

[8]    Chhikara, R. S. and Folks, J. L. (1989). The Inverse Gaussian Distribution, Theory, Methodology and Applications. Marcel Dekker Inc, New-York.

[9]    Chou, C.-W. and Huang, J.-W. (2004). On characterizations of the gamma and the generalized inverse Gaussian distributions. Stat. Probab. Lett. 69, 381–388. MR2091757

[10]    Duerinckx, M., Ley, C. and Swan, Y. (2013). Maximum likelihood characterization of distributions. Bernoulli, to appear. MR3178518

[11]    Eberlein, E. and Hammerstein, E. A. (2004). Generalized hyperbolic and inverse Gaussian distributions: limiting cases and approximation of processes. Prog. Probab. 58, 221–264. MR2096291

[12]    Gauss, C. F. (1809). Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Cambridge Library Collection. Cambridge University Press, Cambridge. Reprint of the 1809 original. MR2858122

[13]    Goldstein, L. and Reinert, G. (2013). Stein’s method for the Beta distribution and the Pòlya-Eggenberger urn. Adv. Appl. Probab., to appear. MR3161381

[14]    Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika 40, 237–260. MR0061330

[15]    Halgreen, C. (1979). Self-decomposability of the generalized inverse Gaussian and hyperbolic distributions. Z. Wahrsch. verw. Geb. 47, 13–17. MR0521527

[16]    Halphen, E. (1941). Sur un nouveau type de courbe de fréquence. Comptes Rendus de l’Académie des Sciences 213, 633–635. Published under the name of “Dugué” due to war constraints. MR0009271

[17]    Hürlimann, W. (1998). On the characterization of maximum likelihood estimators for location-scale families. Comm. Statist. Theory Methods 27, 495–508. MR1621418

[18]    Iyengar, S. and Liao, Q. (1997). Modeling neural activity using the generalized inverse Gaussian distribution. Biol. Cybern. 77, 289–295.

[19]    Jèrgensen, B. (1982). Statistical Properties of the Generalized Inverse Gaussian Distribution. Springer-Verlag, Heidelberg. MR0648107

[20]    Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973). Characterization Problems in Mathematical Statistics. Wiley, New York. MR0346969

[21]    Khatri, C. G. (1962). A characterisation of the inverse Gaussian distribution. Ann. Math. Statist. 33, 800–803. MR0137197

[22]    Kawamura, T. and Kosei, I. (2003). Characterisations of the distributions of power inverse Gaussian and others based on the entropy maximisation principle. J. Japan Statist. Soc. 33, 95–104. MR2044965

[23]    Koudou, A. E. (2006). A link between the Matsumoto-Yor property and an independence property on trees. Stat. Probab. Lett. 76, 1097–1101. MR2269279

[24]    Koudou, A. E. and Ley, C. (2014). Efficiency combined with simplicity: new testing procedures for Generalized Inverse Gaussian models. Test, to appear. DOI: 10.1007/s11749-014-0378-2.

[25]    Koudou, A. E. and Vallois, P. (2011). Which distributions have the Matsumoto-Yor property? Electron. Commun. Prob. 16, 556–566. MR2836761

[26]    Koudou, A. E. and Vallois, P. (2012). Independence properties of the Matsumoto-Yor type. Bernoulli 18, 119–136. MR2888701

[27]    Le Cam, L. and Yang, G. L. (2000). Asymptotics in statistics. Some basic concepts. 2nd ed. Springer-Verlag, New York. MR1784901

[28]    Letac, G. and Mora, M. (1990). Natural real exponential families with cubic variance functions. Ann. Statist. 18, 1–37. MR1041384

[29]    Letac, G. and Seshadri, V. (1983). A characterization of the generalized inverse Gaussian distribution by continued fractions. Z. Wahrsch. Verw. Geb. 62, 485–489. MR0690573

[30]    Letac, G. and Seshadri, V. (1985). On Khatri’s characterization of the inverse Gaussian distribution. Can. J. Stat. 13, 249–252. MR0818329

[31]    Letac, G. and Wesołowski, J. (2000). An independence property for the product of GIG and gamma laws. Ann. Probab. 28, 1371–1383. MR1797878

[32]    Ley, C. and Swan, Y. (2013). Stein’s density approach and information inequalities. Electron. Comm. Probab. 18, 1–14. MR3019670

[33]    Loh, W. L. (1992). Stein’s method and multinomial approximation. Ann. Appl. Probab. 2, 536–554. MR1177898

[34]    Luk, H.-M. (1994). Stein’s method for the gamma distribution and related statistical applications. Ph.D. thesis. University of Southern California. Los Angeles, USA. MR2693204

[35]    Lukacs, E. (1956). Characterization of populations by properties of suitable statistics. Proc. Third Berkeley Symp. on Math. Statist. and Prob., Vol. 2 (Univ. of Calif. Press), 195–214. MR0084892

[36]    Madan, D., Roynette, B. and Yor, M. (2008). Unifying Black-Scholes type formulae which involve Brownian last passage times up to a finite horizon. Asia-Pacific Finan. Markets 15, 97–115.

[37]    Marshall, A. W. and Olkin, I. (1993). Maximum likelihood characterizations of distributions. Statist. Sinica 3, 157–171. MR1219297

[38]    Massam, H. and Wesołowski, J. (2004). The Matsumoto-Yor property on trees. Bernoulli 10, 685–700. MR2076069

[39]    Massam, H. and Wesołowski, J. (2006). The Matsumoto-Yor property and the structure of the Wishart distribution. J. Multivariate Anal. 97, 103–123. MR2208845

[40]    Matsumoto, H. and Yor, M. (2001). An analogue of Pitman’s 2M − X theorem for exponential Wiener functional, Part II: the role of the generalized inverse Gaussian laws. Nagoya Math. J. 162, 65–86. MR1836133

[41]    Matsumoto, H. and Yor, M. (2003). Interpretation via Brownian motion of some independence properties between GIG and Gamma variables. Stat. Probab. Lett. 61, 253–259. MR1959132

[42]    Mudholkar, S. M. and Tian, L. (2002). An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test. J. Stat. Plan. Infer. 102, 211–221. MR1896483

[43]    Peköz, E. (1996). Stein’s method for geometric approximation. J. Appl. Probab. 33, 707–713. MR1401468

[44]    Perreault, L., Bobée, B. and Rasmussen, P. F. (1999a). Halphen distribution system. I: Mathematical and statistical properties. J. Hydrol. Eng. 4, 189–199.

[45]    Perreault, L., Bobée, B. and Rasmussen, P. F. (1999b). Halphen distribution system. II: Parameter and quantile estimation. J. Hydrol. Eng. 4, 200–208.

[46]    Poincaré, H. (1912). Calcul des probabilités. Carré-Naud, Paris.

[47]    Pusz, J. (1997). Regressional characterization of the Generalized inverse Gaussian population. Ann. Inst. Statist. Math. 49, 315–319. MR1463309

[48]    Ross, N. (2011). Fundamentals of Stein’s method. Probab. Surv. 8, 210–293. MR2861132

[49]    Seshadri, V. (1993). The Inverse Gaussian Distribution, a case study in exponential families. Oxford Science Publications. MR1306281

[50]    Seshadri, V. (1999). The Inverse Gaussian Distribution. Springer-Verlag, New York. MR1622488

[51]    Seshadri, V. and Wesołowski, J. (2001). Mutual characterizations of the gamma and the generalized inverse Gaussian laws by constancy of regression. Sankhya Ser. A 63, 107–112. MR1898552

[52]    Seshadri, V. and Wesołowski, J. (2004). Martingales defined by reciprocals of sums and related characterizations. Comm. Statist. Theory Methods 33, 2993–3007. MR2138669

[53]    Shannon, C. E. (1949). The Mathematical Theory of Communication. Wiley, New York.

[54]    Sichel, H. S. (1974). On a distribution representing sentence-length in written prose. J. R. Stat. Soc. Ser. A 137, 25–34.

[55]    Sichel, H. S. (1975). On a distribution law for word frequencies. J. Am. Stat. Assoc. 70, 542–547.

[56]    Stein, C. (1972). A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Vol 2, pp. 586–602). Berkeley: University of California Press. MR0402873

[57]    Stein, C., Diaconis, P., Holmes, S. and Reinert, G. (2004). Use of exchangeable pairs in the analysis of simulations. In Persi Diaconis and Susan Holmes, editors, Stein’s method: expository lectures and applications, volume 46 of IMS Lecture Notes Monogr. Ser, pages 1–26. Beachwood, Ohio, USA: Institute of Mathematical Statistics. MR2118600

[58]    Teicher, H. (1961). Maximum likelihood characterization of distributions. Ann. Math. Statist. 32, 1214–1222. MR0130726

[59]    Vallois, P. (1991). La loi Gaussienne inverse généralisée comme premier ou dernier temps de passage de diffusion. Bull. Sc. Math., 2^e Série, 115, 301–368. MR1117781

[60]    Vasicek, O. (1976). A test for normality based on sample entropy. J. R. Stat. Soc. Ser. B 38, 54–59. MR0420958

[61]    Wesołowski, J. (2002). The Matsumoto-Yor independence property for GIG and Gamma laws, revisited. Math. Proc. Camb. Philos. Soc. 133, 153–161. MR1888812

[62]    Wesołowski, J. and Witkowski, P. (2007). Hitting times of Brownian motion and the Matsumoto-Yor property on trees. Stoch. Proc. Appl. 117, 1303–1315. MR2343941