Multivariate Geometric Stable Laws
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D. N. Anderson, A multivariate Linnik distribution, Statist. Probab. Lett. 14, 333-336 (1992).
D. N. Anderson and B. C. Arnold, Linnik distributions and processes, J. Appl. Probab. 30, 330-340 (1993).
J. Bertoin, Lévy Processes, University Press, Cambridge, 1996.
J. Bunge, Composition semigroups and random stability, Ann. Probab. 24(3), 1476-1489 (1996).
S. Cambanis and W. Wu, Multiple regression on stable vectors, J. Multivariate Anal. 42(2), 243-272 (1992).
L. Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986.
V. Kalashnikov, Geometric Sums: Bounds for Rare Events with Applications, Kluwer Acad. Publ., Dordrecht, 1997.
L. B. Klebanov and S. T. Rachev, Sums of random numbers of random variables and their approximations with v-accompanying infinitely divisible laws, Serdica Math. J. 22, 471-496 (1996).
L. B. Klebanov, G. M. Maniya, and I. A. Melamed, 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, 791-794 (1984).
S. Kotz and I. V. Ostrovskii, A mixture representation of the Linnik distribution, Statist. Probab. Lett. 26, 61-64 (1996).
T. J. Kozubowski, Estimation of the parameters of geometric stable laws, Tech. Rept. No. 253, Department of Statistics and Applied Probability, University of California, Santa Barbara, 1993, to appear in Math. Comput. Modelling.
T. J. Kozubowski, Representation and properties of geometric stable laws, in Approximation, Probability, and Related Fields (G. Anastassiou and S. T. Rachev, eds.), Plenum, New York, 1994, pp. 321-337.
T. J. Kozubowski, The inner characterization of geometric stable laws, Statist. Decisions 12, 307-321 (1994).
T. J. Kozubowski, Characterization of multivariate geometric stable distributions, Statist. Decisions 15, 397-416 (1997).
T. J. Kozubowski, Computer simulation of geometric stable distributions, preprint (1998).
T. J. Kozubowski and S. T. Rachev, The theory of geometric stable distributions and its use in modeling financial data, Europ. J. Oper. Res. 74, 310-324 (1994).
T. J. Kozubowski and A. K. Panorska, On moments and tail behavior of v-stable random variables, Statist. Probab. Lett. 29, 307-315 (1996).
T. J. Kozubowski and A. K. Panorska, Weak limits for multivariate random sums, J. Multivariate Anal., 67, 398-413 (1998).
T. J. Kozubowski and A. K. Panorska, Simulation of geometric stable and other limiting multivariate distributions arising in random summation scheme, Math. Comput. Modelling, in press.
T. J. Kozubowski and A. K. Panorska, Multivariate geometric stable distributions in financial applications, Math. Comput. Modelling, in press.
T. J. Kozubowski, K. Podgórski, and G. Samoroditsky, Tails of Lévy measure of geometric stable random variables, Extremes, 1, 367-378 (1998).
T. J. Kozubowski and S. T. Rachev, Univariate geometric stable laws, J. Comput. Anal. Appl., in press.
M.-L. T. Lee, S. T. Rachev, and G. Samorodnitsky, Dependence of stable random variables, Stochastic Inequalities, IMS Lecture Notes—Monogr. Ser, 22 (M. Shaked and Y. L. Tong, eds.), IMS, Hayward, 1993, pp. 219-234.
A. D. Lisitsky, New expression for characteristic function of multidimentional strictly stable law, in Problems of Stability for Stochastic Models, VNIISI, Moscow, 1990, pp. 49-53 (in Russian).
G. Miller, Properties of certain symmetric stable distributions, J. Multivariate Anal. 8(3), 346-360 (1978).
S. Mittnik and S. T. Rachev, Alternative multivariate stable distributions and their applications to financial modelling, in Stable Processes and Related Topics (S. Cambanis et al., eds.), Birkhaüser, Boston, 1991, pp. 107-119.
I. V. Ostrovskii, Analytic and asymptotic properties of multivariate Linnik's distribution, Math. Phys. Anal. Geometry 2(3/4), 436-455 (1995).
A. G. Pakes, A characterization of gamma mixtures of stable laws motivated by limit theorems, Statist. Neerland. 2–3, 209-218 (1992).
R. N. Pillai, Semi-α-Laplace distributions, Comm. Statist. Theory Methods 14(4), 991-1000 (1985).
R. N. Pillai, On Mittag-Leffler functions and related distributions, Ann. Inst. Statist. Math. 42(1), 157-161 (1990).
S. T. Rachev, Probability Metrics and the Stability of Stochastic Models, Wiley, New York, 1991.
S. T. Rachev and A. SenGupta, Geometric stable distributions and Laplace-Weibull mixtures, Statist. Decisions 10, 251-271 (1992).
G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes, Chapman & Hall, New York, 1994.
R. Weron, On the Chambers-Mallows-Stuck method for simulating skewed stable random variables, Statist. Probab. Lett. 28, 165-171 (1996).