References

• Basu, S.; DasGupta, A. The mean, median, and mode of unimodal distributions: a characterization. Teor. Veroyatnost. i Primenen. 41 (1996), no. 2, 336--352; translation in Theory Probab. Appl. 41 (1996), no. 2, 210--223 (1997) MR1445756
• Bercovici, Hari; Pata, Vittorino. Stable laws and domains of attraction in free probability theory. With an appendix by Philippe Biane. Ann. of Math. (2) 149 (1999), no. 3, 1023--1060. MR1709310
• Bingham, N. H. Limit theorems for occupation times of Markov processes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 17 1971 1--22. MR0281255
• Bingham, N. H. Fluctuation theory in continuous time. Advances in Appl. Probability 7 (1975), no. 4, 705--766. MR0386027
• Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871
• Cressie, Noel. A note on the behaviour of the stable distributions for small index $\alpha $. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 33 (1975/76), no. 1, 61--64. MR0380928
• Demni, Nizar. Kanter random variable and positive free stable distributions. Electron. Commun. Probab. 16 (2011), 137--149. MR2783335
• Dharmadhikari, Sudhakar; Joag-Dev, Kumar. Unimodality, convexity, and applications. Probability and Mathematical Statistics. Academic Press, Inc., Boston, MA, 1988. xiv+278 pp. ISBN: 0-12-214690-5 MR0954608
• A. Erdelyi. Higher transcendental functions. Vol III. McGraw-Hill, 1953.
• Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
• Haubold, H. J.; Mathai, A. M.; Saxena, R. K. Mittag-Leffler functions and their applications. J. Appl. Math. 2011, Art. ID 298628, 51 pp. MR2800586
• Hatzinikitas, Agapitos; Pachos, Jiannis K. One-dimensional stable probability density functions for rational index $0<\alpha\leq 2$. Ann. Physics 323 (2008), no. 12, 3000--3019. MR2467080
• Khoffman-Iënsen, I. Stable densities. (Russian) Teor. Veroyatnost. i Primenen. 38 (1993), no. 2, 470--476; translation in Theory Probab. Appl. 38 (1993), no. 2, 350--355 MR1317993
• Kanter, Marek. Stable densities under change of scale and total variation inequalities. Ann. Probability 3 (1975), no. 4, 697--707. MR0436265
• F. Mainardi. On some properties of the Mittag-Leffler function Ea(-t^a). To appear in Discrete and Continuous Dynamical Systems, Series B. arXiv:1305.0161.
• G. Mittag-Leffler. Sur la nouvelle fonction Ea(x). Comptes Rendus Acad. Sci. Paris 137, 554-558, 1903.
• W. Ml otkowski and K. A. Penson. Probability distributions with binomial moments. arXiv:1309.0595.
• Nagaev, A. V.; Shcolnick, S. M. Properties of mode of spectral positive stable distributions. Stability problems for stochastic models (Varna, 1985), 69--78, Lecture Notes in Math., 1233, Springer, Berlin, 1987. MR0886282
• Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520
• Sato, Ken-iti; Yamazato, Makoto. On distribution functions of class $L$. Z. Wahrsch. Verw. Gebiete 43 (1978), no. 4, 273--308. MR0494405
• Shaked, Moshe; Shanthikumar, J. George. Stochastic orders and their applications. Probability and Mathematical Statistics. Academic Press, Inc., Boston, MA, 1994. xvi+545 pp. ISBN: 0-12-638160-7 MR1278322
• Simon, Thomas. Fonctions de Mittag-Leffler et processus de Lévy stables sans sauts négatifs. (French) [Mittag-Leffler functions and stable Levy processes without negative jumps] Expo. Math. 28 (2010), no. 3, 290--298. MR2671005
• Simon, Thomas. Multiplicative strong unimodality for positive stable laws. Proc. Amer. Math. Soc. 139 (2011), no. 7, 2587--2595. MR2784828
• Simon, Thomas. A multiplicative short proof for the unimodality of stable densities. Electron. Commun. Probab. 16 (2011), 623--629. MR2846655
• Simon, Thomas. On the unimodality of power transformations of positive stable densities. Math. Nachr. 285 (2012), no. 4, 497--506. MR2899640
• Stone, Charles. The set of zeros of a semistable process. Illinois J. Math. 7 1963 631--637. MR0158439
• Williams, E. J. Some representations of stable random variables as products. Biometrika 64 (1977), no. 1, 167--169. MR0448484
• Zolotarev, V. M. One-dimensional stable distributions. Translated from the Russian by H. H. McFaden. Translation edited by Ben Silver. Translations of Mathematical Monographs, 65. American Mathematical Society, Providence, RI, 1986. x+284 pp. ISBN: 0-8218-4519-5 MR0854867
• Zolotarev, V. M. On the representation of the densities of stable laws by special functions. (Russian) Teor. Veroyatnost. i Primenen. 39 (1994), no. 2, 429--437; translation in Theory Probab. Appl. 39 (1994), no. 2, 354--362 (1995) MR1404693