A note on the characterization ofsome minification processes

Wiesław Dziubdziela

Applicationes Mathematicae (1997)

  • Volume: 24, Issue: 4, page 425-428
  • ISSN: 1233-7234

Abstract

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We present a stochastic model which yields a stationary Markov process whose invariant distribution is maximum stable with respect to the geometrically distributed sample size. In particular, we obtain the autoregressive Pareto processes and the autoregressive logistic processes introduced earlier by Yeh et al

How to cite

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Dziubdziela, Wiesław. "A note on the characterization ofsome minification processes." Applicationes Mathematicae 24.4 (1997): 425-428. <http://eudml.org/doc/219182>.

@article{Dziubdziela1997,
abstract = {We present a stochastic model which yields a stationary Markov process whose invariant distribution is maximum stable with respect to the geometrically distributed sample size. In particular, we obtain the autoregressive Pareto processes and the autoregressive logistic processes introduced earlier by Yeh et al},
author = {Dziubdziela, Wiesław},
journal = {Applicationes Mathematicae},
keywords = {logistic process; maximum stability with random sample size; Pareto process; minification process},
language = {eng},
number = {4},
pages = {425-428},
title = {A note on the characterization ofsome minification processes},
url = {http://eudml.org/doc/219182},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Dziubdziela, Wiesław
TI - A note on the characterization ofsome minification processes
JO - Applicationes Mathematicae
PY - 1997
VL - 24
IS - 4
SP - 425
EP - 428
AB - We present a stochastic model which yields a stationary Markov process whose invariant distribution is maximum stable with respect to the geometrically distributed sample size. In particular, we obtain the autoregressive Pareto processes and the autoregressive logistic processes introduced earlier by Yeh et al
LA - eng
KW - logistic process; maximum stability with random sample size; Pareto process; minification process
UR - http://eudml.org/doc/219182
ER -

References

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  1. [1] B. C. Arnold and J. T. Hallett, A characterization of the Pareto process among stationary stochastic processes of the form X n = c min ( X n - 1 , Y n ) , Statist. Probab. Lett. 8 (1989), 377-380. Zbl0686.60029
  2. [2] B. C. Arnold and C. A. Robertson, Autoregressive logistic processes, J. Appl. Probab. 26 (1989), 524-531. Zbl0687.60068
  3. [3] D. P. Gaver and P. A. W. Lewis, First-order autoregressive gamma sequences and point processes, Adv. in Appl. Probab. 12 (1980), 727-745. Zbl0453.60048
  4. [4] S. Janjić, Characterizations of some distributions connected with extremal-type distributions, Publ. Inst. Math. Beograd (N.S.) 39 (53) (1986), 179-186. Zbl0602.62013
  5. [5] V. A. Kalamkar, Minification processes with discrete marginals, J. Appl. Probab. 32 (1995), 692-706. Zbl0834.60076
  6. [6] P. A. W. Lewis and E. McKenzie, Minification processes and their transformations, ibid. 28 (1991), 45-57. Zbl0729.60028
  7. [7] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465. Zbl0727.60039
  8. [8] W. J. Voorn, Characterization of the logistic and loglogistic distributions by extreme value related stability with random sample size, ibid. 24 (1987), 838-851. Zbl0638.62009
  9. [9] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301. Zbl0658.62101

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