Geodesic
Selective lack-of-memory and its application
Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 1, pp. 31-39

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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.
Keywords: discrete distribution, lack-of-memory, selective lack-of-memory, car insurance 
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Stępniak, Czesław. Selective lack-of-memory and its application. Discussiones Mathematicae. Probability and Statistics, Tome 29 (2009) no. 1, pp. 31-39. http://geodesic.mathdoc.fr/item/DMPS_2009_29_1_a1/