A note on the characterization ofsome minification processes

• Autorzy: Wiesław Dziubdziela
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

logistic process; maximum stability with random sample size; Pareto process; minification process

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 4
• Strony: 425-428

Daty

wydano

1997

otrzymano

1996-09-30

Twórcy

autor

Wiesław Dziubdziela

• Institute of Mathematics and Computer Science, Częstochowa Technical University, Dąbrowskiego 73, 42-201 Częstochowa, Poland

Bibliografia

• [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.
• [2] B. C. Arnold and C. A. Robertson, Autoregressive logistic processes, J. Appl. Probab. 26 (1989), 524-531.
• [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.
• [4] S. Janjić, Characterizations of some distributions connected with extremal-type distributions, Publ. Inst. Math. Beograd (N.S.) 39 (53) (1986), 179-186.
• [5] V. A. Kalamkar, Minification processes with discrete marginals, J. Appl. Probab. 32 (1995), 692-706.
• [6] P. A. W. Lewis and E. McKenzie, Minification processes and their transformations, ibid. 28 (1991), 45-57.
• [7] R. N. Pillai, Semi-Pareto processes, ibid. 28 (1991), 461-465.
• [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.
• [9] H. C. Yeh, B. C. Arnold and C. A. Robertson, Pareto processes, ibid. 25 (1988), 291-301.