On the Distributions of Absorbed Particles in Crossing a Field Containing Absorption Points

• Autorzy: Charalambides C. A.
• Języki publikacji: EN

Abstrakty

EN

Consider a queue of particles that are required to cross a field containing a random number of absorption points (traps) acting independently. Suppose that if a particle clashes with (contacts) any of the absorption points, it is absorbed (trapped) with probability p and non absorbed with probability q = 1 - p. Let Xn be the number of absorbed particles from a queue of n particles and Tk the number of particles required to cross the field until the absorption of k particles. Assuming that the number Y of absorption points in the field obeys a q-Poisson distribution (Heine or Euler distribution), the distributions of Xn and Tk are obtained as q-binomial and q-Pascal distributions, respectively. Inversely, assuming thatXn obeys a q-binomial distribution (or, equivalently, assuming that Tk obeys a q-Pascal distribution), the distribution of Y is obtained as a q-Poisson distribution (Heine or Euler distribution).

Słowa kluczowe

EN

absorption distribution; Euler distribution; Heine distribution; inverse absorption distribution; q-binomial distribution; q-Pascal distribution

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2012
• Tom: Vol. 117, nr 1-4
• Strony: 147--154
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Charalambides C. A.

• Department of Mathematics, University of Athens, Panepistemiopolis, GR-15784 Athens, Greece,

Bibliografia

• [1] Barakat, R.: Probabilistic aspects of particles transiting a trapping field: an exact combinatorial solution in terms of Gauss polynomials. J. Appl. Math. and Phys., 36, 1985, 422-432.
• [2] Charalambides, Ch. A.: Discrete q-distributions on Bernoulli trials with a geometrically varying success probability. J. Statist. Plann. Infer., 140, 2010, 2355-2383.
• [3] Zacks, S. and Goldfard, D.: Survival probabilities in crossing a field containing absorption points. Naval Research Logistics Quarterly, 13, 1966, 35-48.