We say that a random variable X taking nonnegative integers has selective lack-of-memory (SLM) property with selector s if P(X ≥ n + s/X ≥ n) = P(X ≥ s) for n = 0,1,.... This property is characterized in an elementary manner by probabilities pₙ = P(X=n). An application in car insurance is presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1105,
author = {Czes\l aw St\k epniak},
title = {Selective lack-of-memory and its application},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {29},
year = {2009},
pages = {31-39},
zbl = {1208.62019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1105}
}
Czesław Stępniak. Selective lack-of-memory and its application. Discussiones Mathematicae Probability and Statistics, Tome 29 (2009) pp. 31-39. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1105/
[000] [1] P. Brémaud, An Introduction to Probabilistic Modeling, 2nd Ed., Springer, New York 1994. | Zbl 0652.60002
[001] [2] S. Chukova and B. Dimitrov, On distributions having the almost-lack-of-memory property, J. Appl. Probab. 29 (1992), 691-698. | Zbl 0752.62010
[002] [3] S. Chukova, B. Dimitrov and D. Green, Probability distributions in periodic random environment and their applications, SIAM J. Appl. Math. 57 (1997), 501-517. | Zbl 0869.60008
[003] [4] S. Chukova, B. Dimitrov and Z. Khalil, A characterization of probability distributions similar to exponential, Canad. J. Statist. 21 (1993), 269-276. | Zbl 0785.62013
[004] [5] S. Chukova and Z. Khalil, On a new characterization of the exponential distribution related to a queueing system with unreliable server, J. Appl. Probab. 27 (1990), 221-226. | Zbl 0704.62011
[005] [6] B. Dimitrov, S. Chukova and Z. Khalil, Definitions, characterizations and structured properties of probability distributions similar to exponential, J. Statist. Plann. Inference 43 (1995), 271-287. | Zbl 0812.62010
[006] [7] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, New York 1968. | Zbl 0155.23101
[007] [8] J. Galambos and S. Kotz, Characterization of Probability Distributions, Springer, Berlin 1978. | Zbl 0381.62011
[008] [9] H. Kulkarni, Characterizations and modelling of multivariate lack of memory property, Metrika 64 (2006), 167-180. | Zbl 1100.62060
[009] [10] G.D. Lin, A note 'On distributions having the almost-lack-of-memory property', J. Appl. Probab. 31 (1993), 854-856. | Zbl 0821.60028
[010] [11] G. Marsaglia and A. Tubilla, A note on the lack of memory property of the exponential distributions, Ann. Probab. 26 (1975), 352-354. | Zbl 0336.60017
[011] [12] C.R. Rao, T. Sapatinas and D.N. Shanbhag, The integrated Cauchy functional equation: some comments on recent papers, Adv. Appl. Probab. 26 (1994), 825-829. | Zbl 0801.62013
[012] [13] D. Roy, On bivariate lack of memory property and a new definition, Ann. Inst. Statist. Math. 54 (2002), 404-410. | Zbl 1012.62011
[013] [14] R. Schimizu, On the lack of memory property of the exponential distribution, Ann. Inst. Statist. Math. 31 (1979), 309-313.
[014] [15] D. Stirzacker, Elementary Probability, Cambridge Univ. Press, Cambridge 1995.
[015] [16] E. Szala, Discrete distributions with partial lack-of-memory, Master's Thesis, University of Rzeszów 2005 (In Polish).