Analytic and Asymptotic Properties of Generalized Linnik Probability Densities

Journal of Mathematical Analysis and Applications

Volumn 217, Issue 2, 1998, Pages 555-578

  Erdogan, M Burak ^a   Ostrovskii, I V ^b  

^a BILKENT UNIVERSITY   (Turkey)

^b B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002400901     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5734     Document Type: Article

References (18)

1. Linnik Ju. V. Linear forms and statistical criteria, I, II. Select. Transl. Math. Statist. Probab. 3:1963;1-90.
2. Arnold B. C. Some characterizations of the exponential distribution by geometric compounding. SIAM J. Appl. Math. 24:1973;242-244.
3. Devroye L. Non-Uniform Random Variable Generation. 1986;Springer-Verlag, New York.
4. Devroye L. A note on Linnik's distribution. Statist. Probab. Lett. 9:1990;305-306.
5. Anderson D. N. A multivariate Linnik distribution. Statist. Probab. Lett. 14:1992;333-336.
6. Anderson D. N., Arnold B. C. Linnik distributions and processes. J. Appl. Probab. 30:1993;330-340.
7. Devroye L. A triptych of discrete distributions related to the stable law. Statist. Probab. Lett. 18:1993;349-351.
8. Kotz S., Ostrovskii I. V., Hayfavi A. Analytic and asymptotic properties of Linnik's probability density, I, II. J. Math. Anal. Appl. 193:1995;353-371.
9. Klebanov L. B., Maniya G. M., Melamed I. A. A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables. Theory Probab. Appl. 29:1984;791-794.
10. Kozubowski T. J. Representation and properties of geometric stable laws. Anastassiou G., Rachev S. T. Approximation, Probability, and Related Fields. 1994;321-327 Plenum, New York.
11. B. Erdogan, Analytic and asymptotic properties of non-symmetric Linnik's densities.
12. Laha R. G. On a class of unimodal distributions. Proc. Amer. Math. Soc. 12:1961;181-184.
13. Pillai R. N. On Mittag-Leffler functions and related distributions. Ann. Inst. Statist. Math. 42:1990;157-161.
14. Pakes A. G. A characterization of gamma mixtures of stable laws motivated by limit theorems. Statist. Neerlandica. 2-3:1992;209-218.
15. Ostrovskii I. V. Analytic and asymptotic properties of multivariate Linnik's distribution. Math. Phys. Anal. Geom. 2:1995;436-455.
16. Yamazato M. Unimodality of infinitely divisible distribution functions of class L. Ann. Probab. 6:1978;523-531.
17. Oxtoby J. C. Measure and Category. 1980;Springer-Verlag, New York/Heidelberg/Berlin.
18. Pólya G., Szegö G. Problems and Theorems in Analysis, II. 1972;Springer-Verlag, New York/Heidelberg/Berlin.