Record Values of a Family of Branching Processes

  • Ibrahim Rahimov
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)


$$ {{\text{X}}_{\text{1}}}\left( {\text{t}} \right){\text{, }}{{\text{X}}_{\text{2}}}\left( {\text{t}} \right), \ldots .,{\text{t}} \in {{\text{N}}_0} = \{ 0,{\text{1,}} \ldots \} $$
, be a sequence of discrete time branching processes. We introduce the following assumptions:
$$ {X_i}\left( t \right),i \geqslant 1 $$
, are independent for any fixed
$$ t \in {N_0}{\text{ and }}{X_i}\left( 0 \right) = 1,i \geqslant 1; $$
$$ P\left\{ {{X_i}\left( t \right) = k\left| {{X_i}\left( 0 \right) = 1} \right.} \right\} = {P_k},k = 0,1, \ldots ,\sum\nolimits_{k = 0}^\infty {{P_k} = 1} $$


Limit Theorem Gamma Distribution Explicit Formula Middle East Critical Case 
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  1. [1]
    Ahsanullah M., Introduction to Record Statistics, Ginn Press, Needham Heights, MA (1988).Google Scholar
  2. [2]
    Athrea K.B., Ney, P.E. Branching process, Springer Verlag (1972).CrossRefGoogle Scholar
  3. [3]
    Nagaraja H.N. Record Values and Related Statistics - a review, Commum. Statist. Theory. Math., 17, pp. 2223–2238 (1988).MathSciNetCrossRefGoogle Scholar
  4. [4]
    Nevzorov V.B. Records, The Theory of Probability and its Application,32, pp. 219–251 (1987).MathSciNetzbMATHGoogle Scholar
  5. [5]
    Slack, R.S. A Branching Process with mean one and possibly infinite variance, Z. Wahzsch. Vezb. Geb. 9(2), pp. 139–145 (1968).MathSciNetCrossRefGoogle Scholar
  6. [6]
    Sevastyanov B.A., Branching Process, Nauka, Moscow (1971).Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ibrahim Rahimov
    • 1
    • 2
  1. 1.Department of Statistics of Middle East Technical UniversityAnkaraTurkey
  2. 2.Mathematical Institute of AS of UzbekistanTashkentTurkey

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