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
@article{bwmeta1.element.bwnjournal-article-zmv24i4p425bwm, author = {Wies\l aw Dziubdziela}, title = {A note on the characterization ofsome minification processes}, journal = {Applicationes Mathematicae}, volume = {24}, year = {1997}, pages = {425-428}, zbl = {0892.60076}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p425bwm} }
Dziubdziela, Wiesław. A note on the characterization ofsome minification processes. Applicationes Mathematicae, Tome 24 (1997) pp. 425-428. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv24i4p425bwm/
[000] [1] B. C. Arnold and J. T. Hallett, A characterization of the Pareto process among stationary stochastic processes of the form , Statist. Probab. Lett. 8 (1989), 377-380. | Zbl 0686.60029
[001] [2] B. C. Arnold and C. A. Robertson, Autoregressive logistic processes, J. Appl. Probab. 26 (1989), 524-531. | Zbl 0687.60068
[002] [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. | Zbl 0453.60048
[003] [4] S. Janjić, Characterizations of some distributions connected with extremal-type distributions, Publ. Inst. Math. Beograd (N.S.) 39 (53) (1986), 179-186. | Zbl 0602.62013
[004] [5] V. A. Kalamkar, Minification processes with discrete marginals, J. Appl. Probab. 32 (1995), 692-706. | Zbl 0834.60076
[005] [6] P. A. W. Lewis and E. McKenzie, Minification processes and their transformations, ibid. 28 (1991), 45-57. | Zbl 0729.60028
[006] [7] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465. | Zbl 0727.60039
[007] [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. | Zbl 0638.62009
[008] [9] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301. | Zbl 0658.62101