Mittag-Leffler process

Mathematical and Computer Modelling

Volumn 37, Issue 12-13, 2003, Pages 1427-1434

  Jayakumar, K ^a  

^a UNIVERSITY OF CALICUT   (India)

Author keywords

Exponential process; Mittag Leffler distribution; River flow time series

Indexed keywords

EID: 0042071534     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(03)90050-1     Document Type: Article

References (19)

1. D.P. Gaver and P.A.W. Lewis, First order autoregressive gamma sequences and point processes, Adv. Appl. Prob. 12, 727-745, (1980).
2. A.J. Lawrance and N.T. Kottegoda, Stochastic modelling of river flow time series (with discussion), J. Roy. Statist. Soc. A 140, 1-47, (1977).
3. C.H. Sim, A mixed gamma ARMA (1,1) model for river flow time series, Water Resources Res. 23, 32-36, (1987).
4. W. Veissman, Jr., G.L. Lewis and J.W. Knapp, Introduction to Hydrology, Third Edition, Harper and Raw, London, (1989).
5. A.J. Lawrance and P.A.W. Lewis, A mixed exponential time series model, Management Sci. 28, 1045-1053, (1982).
6. A.J. Lawrance and P.A.W. Lewis, Generation of some first order autoregressive Markovian sequences of positive random variables with given marginal distribution, In Applied Probability-Computer Science, The Interface, (Edited by R.L. Disney and T.J. Ott), pp. 353-379, (1982).
7. R.N. Pillai, On Mittag-Leffler functions and related distributions, Ann. Inst. Statist. Math. 42, 157-161, (1990).
8. K. Jayakumar and R.N. Pillai, The first order autoregressive Mittag-Leffler process, J. Appl. Prob. 30, 462-466, (1993).
9. R.N. Pillai and K. Jayakumar, Specialized class L property and stationary autoregressive process, Statist. Prob. Letters 19, 51-56, (1994).
10. K. Jayakumar and R.N. Pillai, Characterization of Mittag-Leffler distribution, J. Appl. Statist. Sci. 1, 77-82, (1996).
11. J. Bunge, Composition semigroups and random stability, Ann. Prob. 24, 1476-1489, (1996).
12. K. Jayakumar and R.N. Pillai, Transforms of convolution semigroups, (2001) (to appear).
13. K. Weron and M. Kotulski, On the cole-cole relaxation function and related Mittage-Leffler distributions, Physica A 232, 180-188, (1996).
14. G.D. Lin, On the Mittag-Leffler distributions, J. Statist. Plan. Inference 74, 1-9, (1998).
15. T.J. Kozubowski and S.T. Rachev, Univariate geometric stable laws, J. Comput. Anal. Appl. 1, 177-217, (1999).
16. A.J. Lawrance and P.A.W. Lewis, A new autoregressive time series model in exponential variables, Adv. Appl. Prob. 13, 826-845, (1981).
17. R.N. Pillai, Renewal process with Mittag-Leffler waiting time, Abstract Opsearch 26, 57, (1988).
18. K. Kalyanaraman, SabuGeorge and R.N. Pillai, Monte Carlo studies on Mittag-Leffler distributions and some applications, Unpublished manuscript, (1991).
19. I.A. Ibragimov and K.E. Cherin, On the unimodality of stable laws, Theor. Prob. Appl. 4, 417-419, (1959).