Applications to Stochastic Process and Time Series


Survival Function Weibull Distribution Autoregressive Model Time Series Model Multivariate Normal Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alice, T. and Jose, K. K. (2004). Bivariate semi-Pareto minification processes. Metrika, 59, 305–313.MATHCrossRefMathSciNetGoogle Scholar
  2. Alice, T. and Jose, K. K. (2005). Marshall-Olkin Semi-Weibull Minification Processes. Recent Advances in Statistical Theory and Applications, 1, 6–17.Google Scholar
  3. Anderson, D. N. and Arnold, B. C. (1993). Linnik distributions and processes, J. Appl. Prob., 30, 330–340.MATHCrossRefMathSciNetGoogle Scholar
  4. Arnold, B. C. and Robertson, C. A. (1989). Autoregressive logistic processes. J. Appl. Prob., 26,524–531.MATHCrossRefMathSciNetGoogle Scholar
  5. Berg, C. and Forst, G. (1975). Potential Theory on Locally Compact Abelian Groups, Springer, Berlin.MATHGoogle Scholar
  6. Bondesson, L. (1992). Generalized Gamma Convolutions and Related Classes of Distributions and Densities, Lecture Notes in Statistics 76, Springer–Verlag, New York.MATHGoogle Scholar
  7. Brown, B. G.; Katz, R. W. and Murphy, A. H. (1984). Time series models to simulate and forecast wind speed and wind power. J. Climate Appl. Meteorol. 23, 1184–1195.CrossRefADSGoogle Scholar
  8. Chernick, M. R., Daley, D. J. and Littlejohn, R. P. (1988). A time–reversibility relationship between two Markov chains with stationary exponential distributions, J. Appl. Prob., 25, 418–422.MATHCrossRefMathSciNetGoogle Scholar
  9. Devroye, L. (1990). A note on Linnik’s distribution, Statist. Prob. Letters. 9, 305–306.MATHCrossRefMathSciNetGoogle Scholar
  10. Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York.MATHGoogle Scholar
  11. Fujita, Y. (1993). A generalization of the results of Pillai, Ann. Inst. Statist. Math., 45, 2, 361–365.MATHCrossRefMathSciNetGoogle Scholar
  12. Gaver, D. P. and Lewis, P. A. W. (1980). First order autoregressive gamma sequences and point processes, Adv. Appl. Prob., 12, 727–745.MATHCrossRefMathSciNetGoogle Scholar
  13. Jayakumar, K. and Pillai, R. N. (1993). The first order autoregressive Mittag-Leffler processes, J. Appl. Prob., 30, 462–466.MATHCrossRefMathSciNetGoogle Scholar
  14. Jose, K. K. (1994). Some Aspects of Non-Gaussian Autoregressive Time Series Modeling, Unpublished Ph.D. Thesis submitted to University of Kerala.Google Scholar
  15. Jose, K. K. (2005). Autoregressive models for time series data with exact zeros, (preprint).Google Scholar
  16. Karlin, S. and Taylor, E. (2002) A First Course in Stochastic Processes, Academic press, London.Google Scholar
  17. Klebanov, L. B., Maniya, G. M. and Melamed, I. A. (1985). A problem of Zolotarev and analogues of infinitely divisible and stable distributions in a scheme for summing a random number of random variables, Theory Prob. Appl., 29, 791–794.MATHCrossRefGoogle Scholar
  18. Laha, R. G. and Rohatgi, V. K. (1979). Probability Theory, John Wiley and Sons, New York.MATHGoogle Scholar
  19. Lawrance, A. J. (1991). Directionality and reversibility in time series. Int. Stat. Review, 59(1), 67–79.MathSciNetCrossRefGoogle Scholar
  20. Lawrance, A. J. and Lewis, P. A. W. (1981). A new autoregressive time series model in exponential variables (NEAR(1)), Adv. Appl. Prob., 13, 826–845.MATHCrossRefMathSciNetGoogle Scholar
  21. Lewis, P. A. W. and McKenzie, E. (1991). Minification processes and their transformations. J. Appl. Prob., 28, 45–57.MATHCrossRefMathSciNetGoogle Scholar
  22. Littlejohn, R. P. (1993). A reversibility relation for two Markovian time series models with stationary exponential tailed distribution, J. Appl. Prob., (Preprint).Google Scholar
  23. Marshall, A. W. and Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, 3, 641–652.MATHCrossRefMathSciNetGoogle Scholar
  24. Medhi, A. (2006) Stochastic Models in Queueing Theory, Academic Press, California.Google Scholar
  25. Medhi, A. (2004) Stochastic Processes, New Age Publishers, New Delhi.Google Scholar
  26. Mohan, N. R., Vasudeva, R. and Hebbar, H. V. (1993). On geometrically infinitely divisible laws and geometric domains of attraction, Sankhya B. 55 A, 2, 171–179.MATHMathSciNetGoogle Scholar
  27. Papoulis, E. (2000). Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York.Google Scholar
  28. Pillai, R. N. (1971). Semi-stable laws as limit distributions, Ann. Math. Statist., 42, 2, 780–783.CrossRefMathSciNetGoogle Scholar
  29. Pillai, R. N. (1985). Semi–α–Laplace distributions, Commun. Statist.–Theor. Meth., 14(4), 991–1000.Google Scholar
  30. Pillai, R. N. (1990a). On Mittag-Leffler functions and related distributions, Ann. Inst. Statist. Math., 42, 1, 157–161.MATHCrossRefMathSciNetGoogle Scholar
  31. Pillai, R. N. (1990b). Harmonic mixtures and geometric infinite divisibility, J. Indian Statist. Assoc., 28, 87–98.MathSciNetGoogle Scholar
  32. Pillai, R. N. (1991). Semi–Pareto processes, J. Appl. Prob., 28, 461–465.MATHCrossRefMathSciNetGoogle Scholar
  33. Pillai, R. N. and Sandhya, E. (1990). Distributions with complete monotone derivative and geometric infinite divisibility, Adv. Appl. Prob., 22, 751–754.MATHCrossRefMathSciNetGoogle Scholar
  34. Rachev, S. T. and SenGupta, A. (1992). Geometric stable distributions and Laplace–Weibull mixtures, Statistics and Decisions, 10, 251–271.MATHMathSciNetGoogle Scholar
  35. Ross, S. M. (2002). Probability Models in Stochastics, Academic Press, New Delhi.Google Scholar
  36. Steutel, F.W. (1979). Infinite divisibility in theory and practice, Scand. J. Statist., 6, 57–64.MATHMathSciNetGoogle Scholar
  37. Steutel, F. W. and Van Harn, K. (1979). Discrete analogues of self–decomposability and stability, Ann. Prob., 7, 893–899.MATHCrossRefGoogle Scholar
  38. Tavares, L. V. (1980). An exponential Markovian stationary process. J. Appl. Prob., 17, 1117–1120.MATHCrossRefMathSciNetGoogle Scholar
  39. Yeh, H. C.; Arnold, B. C. and Robertson, C. A. (1988). Pareto processes. J. Appl. Prob., 25, 291–301.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Personalised recommendations