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2009 | 29 | 1 | 31-39
Tytuł artykułu

Selective lack-of-memory and its application

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EN
Abstrakty
EN
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.
Twórcy
  • Institute of Mathematics, University of Rzeszów, Rejtana 16 A, PL-35-959 Rzeszów, Poland
Bibliografia
  • [1] P. Brémaud, An Introduction to Probabilistic Modeling, 2nd Ed., Springer, New York 1994.
  • [2] S. Chukova and B. Dimitrov, On distributions having the almost-lack-of-memory property, J. Appl. Probab. 29 (1992), 691-698.
  • [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.
  • [4] S. Chukova, B. Dimitrov and Z. Khalil, A characterization of probability distributions similar to exponential, Canad. J. Statist. 21 (1993), 269-276.
  • [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.
  • [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.
  • [7] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, New York 1968.
  • [8] J. Galambos and S. Kotz, Characterization of Probability Distributions, Springer, Berlin 1978.
  • [9] H. Kulkarni, Characterizations and modelling of multivariate lack of memory property, Metrika 64 (2006), 167-180.
  • [10] G.D. Lin, A note 'On distributions having the almost-lack-of-memory property', J. Appl. Probab. 31 (1993), 854-856.
  • [11] G. Marsaglia and A. Tubilla, A note on the lack of memory property of the exponential distributions, Ann. Probab. 26 (1975), 352-354.
  • [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.
  • [13] D. Roy, On bivariate lack of memory property and a new definition, Ann. Inst. Statist. Math. 54 (2002), 404-410.
  • [14] R. Schimizu, On the lack of memory property of the exponential distribution, Ann. Inst. Statist. Math. 31 (1979), 309-313.
  • [15] D. Stirzacker, Elementary Probability, Cambridge Univ. Press, Cambridge 1995.
  • [16] E. Szala, Discrete distributions with partial lack-of-memory, Master's Thesis, University of Rzeszów 2005 (In Polish).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1105
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